This version of the adiposity analysis mirrors the birth weight analysis from 09_NPB_Model_BW_v3_MD.R

Some key findings to note:

  • There are fewer participants with complete data on the adiposity outcome and covariates of interest

1 Exploring the data set

The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.

The complete data set for the adiposity outcome consists of n = 780 participants. This represents 67.77% of the original Healthy Start 1 cohort.

Of the 780 participants, 0.26% identify as Latina, 0.17% identify as Black, and 0.26% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 0.51% of babies born were male.

1.1 Exposure data

We have included 19 exposures in our analysis.

These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3), these are based on long-term averages at for each census tract. For mean_pm and mean_o3 are based on the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 8.483046 47.19072       6.006276       43.30893          10128.4962
## [2,] 6.598608 50.05090       7.281109       48.36432          10749.0359
## [3,] 7.454146 48.57052      17.205991       31.67281           9048.6468
## [4,] 6.671239 50.06429       6.842898       45.00359           4223.3434
## [5,] 7.122537 50.14275       3.357792       28.16745            858.7283
## [6,] 7.637453 47.03125      10.743612       45.87564          15603.9800
##      dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,]   2827.538   729.2371          4829.780          7968.654    29116.58
## [2,]   1576.420  5239.2211          4417.792          3780.951    51044.30
## [3,]   3350.303  2992.2968          5211.871          7423.232    36079.21
## [4,]   3364.954  6998.1286          8921.318          9636.816    42235.78
## [5,]   2923.811  3427.2247          7006.042          6806.912    29145.98
## [6,]   3364.200  3166.5395          4484.960          5265.285    43921.85
##      dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,]        1749.1256     275.2480     155.7767          14.377133
## [2,]        7354.5310     279.6435     226.8038           8.905404
## [3,]        4887.2996     221.0414     157.6974           7.636888
## [4,]        3752.6399     203.8812     142.5368           2.850212
## [5,]         729.7784     194.1983     101.0046           5.435988
## [6,]        5870.6867     174.3361     120.3281           5.035971
##      property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,]            37.32935   31.784946 11.529628       26.114650  12.010919
## [2,]            67.03932   15.290231  4.908306        8.500401  18.123496
## [3,]            46.78194    6.891702  4.564963        0.000000   6.307978
## [4,]            21.95270    2.725915  5.623583        1.350621   9.292274
## [5,]            22.49834   12.919186  5.234103        6.307385   2.115768
## [6,]            47.15500    3.842365 10.000000        5.121799  25.171768
##       pct_poc
## [1,] 90.33703
## [2,] 30.44025
## [3,] 26.63305
## [4,] 32.68648
## [5,] 73.60772
## [6,] 23.08698

Variance and histograms of the exposure variables (in their original units):

var(X)
##                             mean_pm        mean_o3 pct_tree_cover
## mean_pm                 0.387935651   -0.006062324    -0.24186797
## mean_o3                -0.006062324    8.955071063    -0.42975173
## pct_tree_cover         -0.241867968   -0.429751728    10.14239201
## pct_impervious          0.374669222   -1.022666581     7.01532904
## mean_aadt_intensity  -244.348900205  303.692966735  9016.25164719
## dist_m_tri           -262.436608185  331.077954338  -208.41963901
## dist_m_npl           -323.917936386  588.917794378   165.47445225
## dist_m_waste_site    -255.868380544  139.101947771  1967.86242644
## dist_m_major_emit      54.696478097  795.943835213   109.80052618
## dist_m_cafo         -1416.446418998 -161.908280851 10579.76974425
## dist_m_mine_well     -346.805134977 -503.738613039  3305.89212551
## cvd_rate_adj            3.764074301    4.075840732   -24.37524733
## res_rate_adj            1.965274289    1.428149656    -1.41491470
## violent_crime_rate      0.155877411    0.749569861    -3.73949960
## property_crime_rate     1.705778861   -1.922286944   -21.72665992
## pct_less_hs             1.150349004    1.853281484    -7.56529205
## pct_unemp               0.055091002    0.506543293    -0.09840703
## pct_limited_eng         0.412512233    1.029344921    -2.79407307
## pct_hh_pov              0.606596961    0.246447334     0.62423227
## pct_poc                 1.697984717    3.441448054   -19.39024560
##                     pct_impervious mean_aadt_intensity    dist_m_tri
## mean_pm                  0.3746692           -244.3489     -262.4366
## mean_o3                 -1.0226666            303.6930      331.0780
## pct_tree_cover           7.0153290           9016.2516     -208.4196
## pct_impervious         179.3785613          56186.2650   -16125.7853
## mean_aadt_intensity  56186.2649588       69165922.5363 -1545741.2032
## dist_m_tri          -16125.7853155       -1545741.2032  6796986.1348
## dist_m_npl           -9073.4066413        1215685.3718  4579262.3957
## dist_m_waste_site    -5149.3668557        1813109.3670  2501094.5398
## dist_m_major_emit     2552.7325419        2477044.2166  1636072.5435
## dist_m_cafo          17731.4297754       15642123.4910  3145985.3646
## dist_m_mine_well      1088.8996239        2146886.0916   937920.3657
## cvd_rate_adj           238.2585184          20288.9695   -51713.8246
## res_rate_adj           182.9073227          34962.3596   -32708.1468
## violent_crime_rate      23.5426763           4766.3910     -848.4942
## property_crime_rate     96.9554914          18227.6819    -3222.6487
## pct_less_hs             59.7110274          -3644.3902   -12701.6695
## pct_unemp               25.7808764           5880.6527    -2452.4569
## pct_limited_eng         42.8626714           2701.0340    -5437.8035
## pct_hh_pov              84.0422503          18597.5270    -8881.9880
## pct_poc                 89.6891621           4493.4912   -18654.6550
##                        dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                 -323.9179         -255.8684          54.69648
## mean_o3                  588.9178          139.1019         795.94384
## pct_tree_cover           165.4745         1967.8624         109.80053
## pct_impervious         -9073.4066        -5149.3669        2552.73254
## mean_aadt_intensity  1215685.3718      1813109.3670     2477044.21655
## dist_m_tri           4579262.3957      2501094.5398     1636072.54352
## dist_m_npl          11347069.4851      4199731.9447     7041775.87881
## dist_m_waste_site    4199731.9447      5299321.7913     1350703.22559
## dist_m_major_emit    7041775.8788      1350703.2256    10385263.63290
## dist_m_cafo          4931146.1458      5617993.1230    -3395813.15490
## dist_m_mine_well      258232.8698      1384614.0282    -1787310.96945
## cvd_rate_adj          -33265.8693       -43188.0097       15096.48910
## res_rate_adj          -19718.2591       -31937.2229       -1526.60012
## violent_crime_rate      -152.7587        -3204.3439         461.39386
## property_crime_rate   -14876.4444       -19362.3191      -20045.85330
## pct_less_hs            -6945.0281       -11539.8973        8548.88251
## pct_unemp               2139.2957        -1457.5039        5159.73353
## pct_limited_eng          432.5398        -4292.4445        9331.34328
## pct_hh_pov             -1451.6169        -7730.1917        8680.72868
## pct_poc                -2074.8078        -8515.4005       21998.02980
##                       dist_m_cafo dist_m_mine_well  cvd_rate_adj  res_rate_adj
## mean_pm                -1416.4464        -346.8051      3.764074      1.965274
## mean_o3                 -161.9083        -503.7386      4.075841      1.428150
## pct_tree_cover         10579.7697        3305.8921    -24.375247     -1.414915
## pct_impervious         17731.4298        1088.8996    238.258518    182.907323
## mean_aadt_intensity 15642123.4910     2146886.0916  20288.969539  34962.359641
## dist_m_tri           3145985.3646      937920.3657 -51713.824619 -32708.146822
## dist_m_npl           4931146.1458      258232.8698 -33265.869348 -19718.259098
## dist_m_waste_site    5617993.1230     1384614.0282 -43188.009668 -31937.222912
## dist_m_major_emit   -3395813.1549    -1787310.9695  15096.489101  -1526.600117
## dist_m_cafo         46839423.7820     9553723.7226 -44601.199501  -7797.531774
## dist_m_mine_well     9553723.7226     4464054.8852 -38076.395520 -14953.132358
## cvd_rate_adj          -44601.1995      -38076.3955   2076.657134   1315.804108
## res_rate_adj           -7797.5318      -14953.1324   1315.804108   1110.806026
## violent_crime_rate       408.3455       -2058.0613    134.891314    100.535111
## property_crime_rate   -18380.9466       -4567.0382    320.604924    290.157212
## pct_less_hs           -24463.8379       -9889.2545    334.637464    201.489440
## pct_unemp               -416.0610       -2620.4519    105.334428     74.963887
## pct_limited_eng        -6285.3923       -4618.3890    185.226339    106.490953
## pct_hh_pov               252.0453       -4667.4525    269.033064    206.556606
## pct_poc               -42540.4506      -24578.3527    619.542560    300.056264
##                     violent_crime_rate property_crime_rate   pct_less_hs
## mean_pm                      0.1558774            1.705779      1.150349
## mean_o3                      0.7495699           -1.922287      1.853281
## pct_tree_cover              -3.7394996          -21.726660     -7.565292
## pct_impervious              23.5426763           96.955491     59.711027
## mean_aadt_intensity       4766.3910356        18227.681901  -3644.390223
## dist_m_tri                -848.4941529        -3222.648703 -12701.669456
## dist_m_npl                -152.7586849       -14876.444381  -6945.028107
## dist_m_waste_site        -3204.3438644       -19362.319083 -11539.897288
## dist_m_major_emit          461.3938611       -20045.853299   8548.882507
## dist_m_cafo                408.3455047       -18380.946611 -24463.837868
## dist_m_mine_well         -2058.0613390        -4567.038163  -9889.254521
## cvd_rate_adj               134.8913140          320.604924    334.637464
## res_rate_adj               100.5351114          290.157212    201.489440
## violent_crime_rate          36.5195077          135.346154     25.285073
## property_crime_rate        135.3461545         1160.236223      3.004961
## pct_less_hs                 25.2850735            3.004961    163.762734
## pct_unemp                   12.0566338            3.018063     40.254624
## pct_limited_eng             14.1433364          -11.409839     86.491751
## pct_hh_pov                  30.5537434           63.667397    103.102830
## pct_poc                     52.0085020          -26.369164    241.514049
##                          pct_unemp pct_limited_eng    pct_hh_pov       pct_poc
## mean_pm                 0.05509100       0.4125122     0.6065970      1.697985
## mean_o3                 0.50654329       1.0293449     0.2464473      3.441448
## pct_tree_cover         -0.09840703      -2.7940731     0.6242323    -19.390246
## pct_impervious         25.78087638      42.8626714    84.0422503     89.689162
## mean_aadt_intensity  5880.65274910    2701.0340348 18597.5269669   4493.491248
## dist_m_tri          -2452.45686782   -5437.8034938 -8881.9879579 -18654.655039
## dist_m_npl           2139.29571806     432.5397585 -1451.6169481  -2074.807832
## dist_m_waste_site   -1457.50390263   -4292.4445272 -7730.1916796  -8515.400484
## dist_m_major_emit    5159.73353103    9331.3432771  8680.7286763  21998.029803
## dist_m_cafo          -416.06100829   -6285.3922771   252.0452517 -42540.450615
## dist_m_mine_well    -2620.45185414   -4618.3890431 -4667.4524666 -24578.352704
## cvd_rate_adj          105.33442831     185.2263391   269.0330637    619.542560
## res_rate_adj           74.96388699     106.4909525   206.5566058    300.056264
## violent_crime_rate     12.05663378      14.1433364    30.5537434     52.008502
## property_crime_rate     3.01806326     -11.4098394    63.6673970    -26.369164
## pct_less_hs            40.25462427      86.4917511   103.1028300    241.514049
## pct_unemp              24.70089342      25.8002340    37.9257486     73.691783
## pct_limited_eng        25.80023399      69.4638469    69.0402541    143.757101
## pct_hh_pov             37.92574856      69.0402541   122.9753676    158.037277
## pct_poc                73.69178348     143.7571008   158.0372769    530.391699
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,]  1.63895222 -0.2235917    -0.09106707      0.2355128        -0.004372722
## [2,] -1.38658135  0.7321879     0.30923073      0.6129716         0.070241827
## [3,] -0.01298527  0.2374938     3.42564459     -0.6332930        -0.134215290
## [4,] -1.26996939  0.7366655     0.17163233      0.3620440        -0.714416377
## [5,] -0.54539411  0.7628814    -0.92269126     -0.8950193        -1.118982302
## [6,]  0.28132089 -0.2768817     1.39645679      0.4271554         0.654006942
##      dist_m_tri  dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] -0.3966655 -1.41524068      -0.158944386       -0.09829063  -1.1211055
## [2,] -0.8765539 -0.07638689      -0.337912010       -1.39776302   2.0828583
## [3,] -0.1961498 -0.74341877       0.007035929       -0.26753873  -0.1037626
## [4,] -0.1905302  0.44577016       1.618419775        0.41935153   0.7958031
## [5,] -0.3597382 -0.61430417       0.786424074       -0.45878682  -1.1168106
## [6,] -0.1908194 -0.69169232      -0.308734136       -0.93716429   1.0421630
##      dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,]       -0.7694006    0.6888535   -0.2667071          0.2857705
## [2,]        1.8836300    0.7853085    1.8643986         -0.6196746
## [3,]        0.7158928   -0.5006603   -0.2090789         -0.8295849
## [4,]        0.1788599   -0.8772257   -0.6639585         -1.6216694
## [5,]       -1.2518563   -1.0897090   -1.9100974         -1.1937830
## [6,]        1.1813285   -1.5255654   -1.3303122         -1.2599766
##      property_crime_rate pct_less_hs   pct_unemp pct_limited_eng pct_hh_pov
## [1,]          -0.5116110  1.20006290  0.38269452      2.15729293 -0.2815741
## [2,]           0.3606149 -0.08889067 -0.94956352      0.04387831  0.2696336
## [3,]          -0.2341017 -0.74518055 -1.01864671     -0.97602734 -0.7958425
## [4,]          -0.9630391 -1.07070943 -0.80564470     -0.81397542 -0.5267306
## [5,]          -0.9470203 -0.27417225 -0.88401077     -0.21924683 -1.1738791
## [6,]          -0.2231493 -0.98346622  0.07492226     -0.36149732  0.9052185
##         pct_poc
## [1,]  1.5763100
## [2,] -1.0244789
## [3,] -1.1897923
## [4,] -0.9269452
## [5,]  0.8499036
## [6,] -1.3437665

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3 pct_tree_cover pct_impervious
## mean_pm              1.000000000 -0.003252556   -0.121934980     0.04491412
## mean_o3             -0.003252556  1.000000000   -0.045093393    -0.02551610
## pct_tree_cover      -0.121934980 -0.045093393    1.000000000     0.16447223
## pct_impervious       0.044914121 -0.025516099    0.164472230     1.00000000
## mean_aadt_intensity -0.047172018  0.012202649    0.340415825     0.50442756
## dist_m_tri          -0.161616753  0.042436304   -0.025102111    -0.46182497
## dist_m_npl          -0.154387912  0.058422253    0.015424777    -0.20111444
## dist_m_waste_site   -0.178454140  0.020192428    0.268419703    -0.16701613
## dist_m_major_emit    0.027250266  0.082535188    0.010698563     0.05914408
## dist_m_cafo         -0.332287904 -0.007905490    0.485400532     0.19344287
## dist_m_mine_well    -0.263536583 -0.079672044    0.491307868     0.03848024
## cvd_rate_adj         0.132616005  0.029888236   -0.167956353     0.39037390
## res_rate_adj         0.094672580  0.014319244   -0.013330331     0.40975731
## violent_crime_rate   0.041413399  0.041449103   -0.194303596     0.29087615
## property_crime_rate  0.080402522 -0.018858645   -0.200285524     0.21252691
## pct_less_hs          0.144325222  0.048394870   -0.185629913     0.34838683
## pct_unemp            0.017796906  0.034058516   -0.006217268     0.38730765
## pct_limited_eng      0.079465308  0.041271190   -0.105266007     0.38398526
## pct_hh_pov           0.087823617  0.007426438    0.017675307     0.56585263
## pct_poc              0.118373795  0.049935378   -0.264371573     0.29077451
##                     mean_aadt_intensity  dist_m_tri   dist_m_npl
## mean_pm                     -0.04717202 -0.16161675 -0.154387912
## mean_o3                      0.01220265  0.04243630  0.058422253
## pct_tree_cover               0.34041583 -0.02510211  0.015424777
## pct_impervious               0.50442756 -0.46182497 -0.201114438
## mean_aadt_intensity          1.00000000 -0.07129064  0.043394356
## dist_m_tri                  -0.07129064  1.00000000  0.521429359
## dist_m_npl                   0.04339436  0.52142936  1.000000000
## dist_m_waste_site            0.09470388  0.41673672  0.541588668
## dist_m_major_emit            0.09242275  0.19473123  0.648681599
## dist_m_cafo                  0.27481716  0.17631641  0.213894809
## dist_m_mine_well             0.12217945  0.17027191  0.036283143
## cvd_rate_adj                 0.05353422 -0.43527735 -0.216707839
## res_rate_adj                 0.12613498 -0.37642515 -0.175633598
## violent_crime_rate           0.09483772 -0.05385527 -0.007504152
## property_crime_rate          0.06434461 -0.03628955 -0.129653449
## pct_less_hs                 -0.03424296 -0.38071069 -0.161110784
## pct_unemp                    0.14227321 -0.18927221  0.127782869
## pct_limited_eng              0.03896768 -0.25025681  0.015406527
## pct_hh_pov                   0.20165084 -0.30721536 -0.038859849
## pct_poc                      0.02346062 -0.31069243 -0.026744696
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.17845414        0.02725027 -0.332287904
## mean_o3                    0.02019243        0.08253519 -0.007905490
## pct_tree_cover             0.26841970        0.01069856  0.485400532
## pct_impervious            -0.16701613        0.05914408  0.193442865
## mean_aadt_intensity        0.09470388        0.09242275  0.274817163
## dist_m_tri                 0.41673672        0.19473123  0.176316410
## dist_m_npl                 0.54158867        0.64868160  0.213894809
## dist_m_waste_site          1.00000000        0.18207111  0.356586819
## dist_m_major_emit          0.18207111        1.00000000 -0.153967569
## dist_m_cafo                0.35658682       -0.15396757  1.000000000
## dist_m_mine_well           0.28467794       -0.26249836  0.660696709
## cvd_rate_adj              -0.41169031        0.10279803 -0.143007353
## res_rate_adj              -0.41626308       -0.01421338 -0.034184739
## violent_crime_rate        -0.23033849        0.02369194  0.009873237
## property_crime_rate       -0.24693009       -0.18261758 -0.078847675
## pct_less_hs               -0.39172768        0.20729701 -0.279325946
## pct_unemp                 -0.12739232        0.32215300 -0.012231928
## pct_limited_eng           -0.22372532        0.34742094 -0.110191273
## pct_hh_pov                -0.30281059        0.24290606  0.003320960
## pct_poc                   -0.16061887        0.29639895 -0.269896936
##                     dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm                  -0.26353658   0.13261601   0.09467258
## mean_o3                  -0.07967204   0.02988824   0.01431924
## pct_tree_cover            0.49130787  -0.16795635  -0.01333033
## pct_impervious            0.03848024   0.39037390   0.40975731
## mean_aadt_intensity       0.12217945   0.05353422   0.12613498
## dist_m_tri                0.17027191  -0.43527735  -0.37642515
## dist_m_npl                0.03628314  -0.21670784  -0.17563360
## dist_m_waste_site         0.28467794  -0.41169031  -0.41626308
## dist_m_major_emit        -0.26249836   0.10279803  -0.01421338
## dist_m_cafo               0.66069671  -0.14300735  -0.03418474
## dist_m_mine_well          1.00000000  -0.39546556  -0.21234806
## cvd_rate_adj             -0.39546556   1.00000000   0.86634271
## res_rate_adj             -0.21234806   0.86634271   1.00000000
## violent_crime_rate       -0.16118740   0.48982295   0.49915588
## property_crime_rate      -0.06345950   0.20654495   0.25558834
## pct_less_hs              -0.36575582   0.57383181   0.47241713
## pct_unemp                -0.24954857   0.46508423   0.45256051
## pct_limited_eng          -0.26226862   0.48768672   0.38336652
## pct_hh_pov               -0.19920768   0.53237076   0.55887015
## pct_poc                  -0.50511428   0.59032393   0.39091760
##                     violent_crime_rate property_crime_rate pct_less_hs
## mean_pm                    0.041413399          0.08040252  0.14432522
## mean_o3                    0.041449103         -0.01885865  0.04839487
## pct_tree_cover            -0.194303596         -0.20028552 -0.18562991
## pct_impervious             0.290876145          0.21252691  0.34838683
## mean_aadt_intensity        0.094837724          0.06434461 -0.03424296
## dist_m_tri                -0.053855270         -0.03628955 -0.38071069
## dist_m_npl                -0.007504152         -0.12965345 -0.16111078
## dist_m_waste_site         -0.230338488         -0.24693009 -0.39172768
## dist_m_major_emit          0.023691938         -0.18261758  0.20729701
## dist_m_cafo                0.009873237         -0.07884767 -0.27932595
## dist_m_mine_well          -0.161187402         -0.06345950 -0.36575582
## cvd_rate_adj               0.489822949          0.20654495  0.57383181
## res_rate_adj               0.499155881          0.25558834  0.47241713
## violent_crime_rate         1.000000000          0.65752195  0.32695970
## property_crime_rate        0.657521947          1.00000000  0.00689379
## pct_less_hs                0.326959697          0.00689379  1.00000000
## pct_unemp                  0.401427649          0.01782784  0.63292450
## pct_limited_eng            0.280808338         -0.04019082  0.81093815
## pct_hh_pov                 0.455924473          0.16855235  0.72653072
## pct_poc                    0.373691766         -0.03361436  0.81947649
##                        pct_unemp pct_limited_eng   pct_hh_pov     pct_poc
## mean_pm              0.017796906      0.07946531  0.087823617  0.11837380
## mean_o3              0.034058516      0.04127119  0.007426438  0.04993538
## pct_tree_cover      -0.006217268     -0.10526601  0.017675307 -0.26437157
## pct_impervious       0.387307652      0.38398526  0.565852631  0.29077451
## mean_aadt_intensity  0.142273206      0.03896768  0.201650845  0.02346062
## dist_m_tri          -0.189272211     -0.25025681 -0.307215358 -0.31069243
## dist_m_npl           0.127782869      0.01540653 -0.038859849 -0.02674470
## dist_m_waste_site   -0.127392321     -0.22372532 -0.302810585 -0.16061887
## dist_m_major_emit    0.322153000      0.34742094  0.242906063  0.29639895
## dist_m_cafo         -0.012231928     -0.11019127  0.003320960 -0.26989694
## dist_m_mine_well    -0.249548573     -0.26226862 -0.199207679 -0.50511428
## cvd_rate_adj         0.465084229      0.48768672  0.532370759  0.59032393
## res_rate_adj         0.452560508      0.38336652  0.558870145  0.39091760
## violent_crime_rate   0.401427649      0.28080834  0.455924473  0.37369177
## property_crime_rate  0.017827843     -0.04019082  0.168552353 -0.03361436
## pct_less_hs          0.632924498      0.81093815  0.726530718  0.81947649
## pct_unemp            1.000000000      0.62285635  0.688127265  0.64381987
## pct_limited_eng      0.622856353      1.00000000  0.746988474  0.74894777
## pct_hh_pov           0.688127265      0.74698847  1.000000000  0.61880258
## pct_poc              0.643819872      0.74894777  0.618802578  1.00000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.2 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

NOTE: It’ll be interesting to see what comes out of our BEAMERS discussion re: adjusting for gestational age. It’s currently in the analysis

There are four continuous covariates; all of the others have been coded as dummy variables. For the dummy variables, the reference groups are: white_re, ed_grad, norm_bmi

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            latina_re, black_re, other_re,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w, days_to_peapod) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133   -4170.944         1        0        0        0     0
## [2,] 39.62671 -104.9927   -4160.517         0        0        1        0     0
## [3,] 39.74934 -104.9129   -4170.219         0        0        0        0     0
## [4,] 39.68397 -104.8933   -4162.583         0        0        0        0     0
## [5,] 39.79134 -104.7669   -4168.814         0        1        0        0     0
## [6,] 39.68050 -104.9451   -4164.274         1        0        0        0     0
##      ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     1      0       0        0         0             0             0
## [2,]     1      0       0        0         0             0             0
## [3,]     0      0       0        0         0             0             0
## [4,]     1      0       0        0         0             1             0
## [5,]     0      1       0        0         0             1             0
## [6,]     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0           19
## [2,]           0           1           0           0           0           36
## [3,]           0           1           0           0           0           34
## [4,]           0           1           0           0           0           28
## [5,]           0           1           0           0           0           30
## [6,]           0           1           0           0           0           22
##      any_smoker smokeSH mean_cpss mean_epsd male gest_age_w days_to_peapod
## [1,]          0       1        29         0    0   40.57143              1
## [2,]          0       0        19         2    1   35.85714              2
## [3,]          0       0        19         1    0   40.42857              2
## [4,]          0       0        20         0    0   36.28571              1
## [5,]          0       0        15         0    1   38.42857              2
## [6,]          0       0        17         1    0   40.71429              1

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "gest_age_w"     "days_to_peapod"
W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27, 28)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:20], W.s[,4],
                  W[,22:23], W.s[,5:6],
                  W[,26], W.s[,7:8])
colnames(W.scaled)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] ""               "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      ""               "gest_age_w"     "days_to_peapod"
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,]  0.9582490  0.5369709  -0.5836483         1        0        0        0
## [2,] -1.5595136 -1.6096907   0.6608980         0        0        1        0
## [3,]  0.2858292 -0.6547167  -0.4971411         0        0        0        0
## [4,] -0.6978905 -0.4200223   0.4143032         0        0        0        0
## [5,]  0.9178908  1.0931096  -0.3293688         0        1        0        0
## [6,] -0.7500299 -1.0397812   0.2123849         1        0        0        0
##      ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     0     1      0       0        0         0             0             0
## [2,]     0     1      0       0        0         0             0             0
## [3,]     0     0      0       0        0         0             0             0
## [4,]     0     1      0       0        0         0             1             0
## [5,]     0     0      1       0        0         0             1             0
## [6,]     0     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0  -1.41994612
## [2,]           0           1           0           0           0   1.35302672
## [3,]           0           1           0           0           0   1.02679462
## [4,]           0           1           0           0           0   0.04809832
## [5,]           0           1           0           0           0   0.37433042
## [6,]           0           1           0           0           0  -0.93059797
##      any_smoker smokeSH  mean_cpss  mean_epsd male gest_age_w days_to_peapod
## [1,]          0       1  3.3968005 -1.3157360    0  0.8044835     -0.2392302
## [2,]          0       0  0.1208193 -0.6918928    1 -2.7388783      0.1867962
## [3,]          0       0  0.1208193 -1.0038144    0  0.6971089      0.1867962
## [4,]          0       0  0.4484174 -1.3157360    0 -2.4167545     -0.2392302
## [5,]          0       0 -1.1895732 -1.3157360    1 -0.8061355      0.1867962
## [6,]          0       0 -0.5343769 -1.0038144    0  0.9118581     -0.2392302
summary(W.scaled)
##       lat                lon           lat_lon_int          latina_re     
##  Min.   :-2.46715   Min.   :-2.4830   Min.   :-3.510301   Min.   :0.0000  
##  1st Qu.:-0.62450   1st Qu.:-0.5811   1st Qu.:-0.493286   1st Qu.:0.0000  
##  Median : 0.05945   Median : 0.1064   Median : 0.008488   Median :0.0000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.000000   Mean   :0.2628  
##  3rd Qu.: 0.43089   3rd Qu.: 0.6643   3rd Qu.: 0.599123   3rd Qu.:1.0000  
##  Max.   : 4.01365   Max.   : 4.5155   Max.   : 2.628224   Max.   :1.0000  
##     black_re         other_re          ed_no_hs          ed_hs       
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.1654   Mean   :0.06667   Mean   :0.1538   Mean   :0.1833  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##      ed_aa            ed_4yr          low_bmi           ovwt_bmi     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
##  Mean   :0.2256   Mean   :0.2205   Mean   :0.03077   Mean   :0.2615  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.0000  
##    obese_bmi      concep_spring    concep_summer   concep_fall    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.00   Median :0.0000  
##  Mean   :0.1962   Mean   :0.2436   Mean   :0.25   Mean   :0.2667  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.25   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00   Max.   :1.0000  
##   concep_2010      concep_2011      concep_2012      concep_2013    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1692   Mean   :0.2936   Mean   :0.2808   Mean   :0.2551  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   maternal_age       any_smoker         smokeSH         mean_cpss       
##  Min.   :-1.9093   Min.   :0.00000   Min.   :0.0000   Min.   :-6.10355  
##  1st Qu.:-0.9306   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:-0.53438  
##  Median : 0.0481   Median :0.00000   Median :0.0000   Median : 0.01162  
##  Mean   : 0.0000   Mean   :0.08718   Mean   :0.2474   Mean   : 0.00000  
##  3rd Qu.: 0.7006   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.: 0.55762  
##  Max.   : 2.6580   Max.   :1.00000   Max.   :1.0000   Max.   : 3.39680  
##    mean_epsd            male          gest_age_w       days_to_peapod   
##  Min.   :-1.3157   Min.   :0.0000   Min.   :-5.20849   Min.   :-0.6653  
##  1st Qu.:-0.7959   1st Qu.:0.0000   1st Qu.:-0.48401   1st Qu.:-0.2392  
##  Median :-0.1720   Median :1.0000   Median : 0.05286   Median :-0.2392  
##  Mean   : 0.0000   Mean   :0.5064   Mean   : 0.00000   Mean   : 0.0000  
##  3rd Qu.: 0.5558   3rd Qu.:1.0000   3rd Qu.: 0.69711   3rd Qu.:-0.2392  
##  Max.   : 3.9869   Max.   :1.0000   Max.   : 3.81097   Max.   :10.4114

Variance and histograms for the scaled covariates

var(W.scaled)
##                          lat           lon  lat_lon_int      latina_re
## lat             1.0000000000 -0.2294265015 -0.922594810  0.01488040464
## lon            -0.2294265015  1.0000000000  0.587147326  0.00774099102
## lat_lon_int    -0.9225948101  0.5871473257  1.000000000 -0.00928638293
## latina_re       0.0148804046  0.0077409910 -0.009286383  0.19399460189
## black_re       -0.0076765642  0.0416993781  0.022926625 -0.04352226721
## other_re        0.0022244292 -0.0045513219 -0.003662305 -0.01754385965
## ed_no_hs       -0.0002536098  0.0211421973  0.008600587  0.03781968994
## ed_hs          -0.0092915161  0.0376437998  0.022660243  0.03262729996
## ed_aa          -0.0072973858  0.0461167337  0.024355069  0.01250781739
## ed_4yr          0.0084748321 -0.0053108878 -0.009175293 -0.03620683980
## low_bmi        -0.0031399188  0.0031935883  0.003878110 -0.00167868075
## ovwt_bmi        0.0176550362  0.0102854255 -0.010619251  0.02488397354
## obese_bmi       0.0151602612  0.0074254851 -0.009652703  0.02283499556
## concep_spring   0.0203171932 -0.0022492530 -0.017790516 -0.00633619697
## concep_summer  -0.0229599220 -0.0001995618  0.019015261 -0.00417201540
## concep_fall     0.0095582094  0.0161897319 -0.001540859  0.01583226359
## concep_2010     0.0109529805  0.0028301792 -0.008007944 -0.00859089563
## concep_2011    -0.0226544797  0.0224924333  0.027745587 -0.01050821237
## concep_2012     0.0015394008 -0.0023870971 -0.002215499  0.01340475955
## concep_2013     0.0089319968 -0.0236248234 -0.016772917  0.00474803331
## maternal_age    0.0348578763 -0.1930103076 -0.105532928 -0.11130236864
## any_smoker     -0.0069992076  0.0222429459  0.014635045 -0.00753760574
## smokeSH         0.0011347413  0.0442610839  0.016595995 -0.00349725157
## mean_cpss      -0.0279187887 -0.0046586574  0.021381618 -0.04032749691
## mean_epsd      -0.0458873302  0.0573784314  0.060923471  0.03908431534
## male            0.0224103855 -0.0245595335 -0.028364840  0.00152233304
## gest_age_w      0.0302744587 -0.0833518477 -0.058256588 -0.00772944439
## days_to_peapod  0.0166177524 -0.0037582676 -0.015297436 -0.00006310256
##                     black_re      other_re      ed_no_hs         ed_hs
## lat            -0.0076765642  0.0022244292 -0.0002536098 -0.0092915161
## lon             0.0416993781 -0.0045513219  0.0211421973  0.0376437998
## lat_lon_int     0.0229266248 -0.0036623054  0.0086005874  0.0226602429
## latina_re      -0.0435222672 -0.0175438596  0.0378196899  0.0326273000
## black_re        0.1382097363 -0.0110397946  0.0143181594  0.0158536585
## other_re       -0.0110397946  0.0623020967 -0.0025673941  0.0031664527
## ed_no_hs        0.0143181594 -0.0025673941  0.1303446233 -0.0282413350
## ed_hs           0.0158536585  0.0031664527 -0.0282413350  0.1499144202
## ed_aa           0.0178335144  0.0041934104 -0.0347585662 -0.0414206247
## ed_4yr         -0.0172607880 -0.0031664527 -0.0339685988 -0.0404792469
## low_bmi         0.0026068925 -0.0007702182 -0.0034561074 -0.0005134788
## ovwt_bmi        0.0003357362 -0.0059050064  0.0046410586 -0.0069319641
## obese_bmi       0.0073121359  0.0023106547  0.0057272638  0.0268934531
## concep_spring  -0.0005431026  0.0055626872 -0.0028636319  0.0014976466
## concep_summer  -0.0067394095  0.0000000000 -0.0038510911 -0.0060975610
## concep_fall    -0.0069319641 -0.0023962345  0.0102695764  0.0062473256
## concep_2010     0.0117705145 -0.0010269576  0.0008887133  0.0074454429
## concep_2011     0.0155672953 -0.0003423192  0.0112570356 -0.0063970903
## concep_2012    -0.0118346993 -0.0007702182 -0.0047398045  0.0062259307
## concep_2013    -0.0152908068  0.0022250749 -0.0072084527 -0.0070389388
## maternal_age   -0.0914960717 -0.0135406562 -0.1473311448 -0.1061266380
## any_smoker      0.0150883776 -0.0006846384  0.0173792831  0.0045357296
## smokeSH         0.0321961094  0.0065896448  0.0324874099  0.0251818571
## mean_cpss      -0.0362044396  0.0225734779 -0.0574356146 -0.0356451617
## mean_epsd       0.0160927464  0.0210839610  0.0715352956  0.0221439428
## male           -0.0055544584  0.0021394951 -0.0151081268  0.0007488233
## gest_age_w     -0.0459673981 -0.0051550835 -0.0121190054 -0.0148312028
## days_to_peapod  0.0353079864  0.0037188443  0.0068992133  0.0014765999
##                       ed_aa        ed_4yr       low_bmi      ovwt_bmi
## lat            -0.007297386  0.0084748321 -0.0031399188  0.0176550362
## lon             0.046116734 -0.0053108878  0.0031935883  0.0102854255
## lat_lon_int     0.024355069 -0.0091752931  0.0038781104 -0.0106192507
## latina_re       0.012507817 -0.0362068398 -0.0016786808  0.0248839735
## black_re        0.017833514 -0.0172607880  0.0026068925  0.0003357362
## other_re        0.004193410 -0.0031664527 -0.0007702182 -0.0059050064
## ed_no_hs       -0.034758566 -0.0339685988 -0.0034561074  0.0046410586
## ed_hs          -0.041420625 -0.0404792469 -0.0005134788 -0.0069319641
## ed_aa           0.174951450 -0.0498206116  0.0046015602  0.0179322603
## ed_4yr         -0.049820612  0.1721075672 -0.0003752345  0.0013034462
## low_bmi         0.004601560 -0.0003752345  0.0298607682 -0.0080576676
## ovwt_bmi        0.017932260  0.0013034462 -0.0080576676  0.1933840229
## obese_bmi       0.012165498 -0.0137849314 -0.0060432507 -0.0513676311
## concep_spring   0.006583062 -0.0062868240 -0.0049372963  0.0068134689
## concep_summer  -0.010269576  0.0089858793  0.0038510911 -0.0051347882
## concep_fall    -0.010183997  0.0014548567  0.0033376123  0.0046213094
## concep_2010     0.002843883  0.0011454528  0.0024883974 -0.0032388664
## concep_2011     0.002988710  0.0057799282  0.0025081465  0.0065567295
## concep_2012    -0.005668016 -0.0067937198 -0.0047990520 -0.0054902735
## concep_2013    -0.001158619  0.0001514104 -0.0001579935  0.0025081465
## maternal_age   -0.034152305  0.1077776102 -0.0091971230  0.0067327450
## any_smoker      0.008544814 -0.0153977815  0.0011652019 -0.0048582996
## smokeSH         0.021118462 -0.0353773740  0.0026463908 -0.0108818011
## mean_cpss       0.029189204  0.0275174804  0.0079977462 -0.0043164323
## mean_epsd       0.016391602 -0.0481925954  0.0107834260  0.0098080614
## male            0.001119121  0.0062868240 -0.0001974919 -0.0029623778
## gest_age_w     -0.025824190  0.0330362179 -0.0033335217 -0.0159296533
## days_to_peapod  0.025249438 -0.0107106080 -0.0073703791 -0.0139751139
##                   obese_bmi concep_spring concep_summer   concep_fall
## lat             0.015160261  0.0203171932 -0.0229599220  0.0095582094
## lon             0.007425485 -0.0022492530 -0.0001995618  0.0161897319
## lat_lon_int    -0.009652703 -0.0177905156  0.0190152613 -0.0015408589
## latina_re       0.022834996 -0.0063361970 -0.0041720154  0.0158322636
## black_re        0.007312136 -0.0005431026 -0.0067394095 -0.0069319641
## other_re        0.002310655  0.0055626872  0.0000000000 -0.0023962345
## ed_no_hs        0.005727264 -0.0028636319 -0.0038510911  0.0102695764
## ed_hs           0.026893453  0.0014976466 -0.0060975610  0.0062473256
## ed_aa           0.012165498  0.0065830618 -0.0102695764 -0.0101839966
## ed_4yr         -0.013784931 -0.0062868240  0.0089858793  0.0014548567
## low_bmi        -0.006043251 -0.0049372963  0.0038510911  0.0033376123
## ovwt_bmi       -0.051367631  0.0068134689 -0.0051347882  0.0046213094
## obese_bmi       0.157879925 -0.0029130048 -0.0054557125 -0.0048780488
## concep_spring  -0.002913005  0.1844903064 -0.0609756098 -0.0650406504
## concep_summer  -0.005455712 -0.0609756098  0.1877406932 -0.0667522465
## concep_fall    -0.004878049 -0.0650406504 -0.0667522465  0.1958065896
## concep_2010    -0.004996544 -0.0233040387  0.0012836970  0.0267008986
## concep_2011     0.002671077  0.0041308713 -0.0003209243 -0.0129225503
## concep_2012     0.009040190 -0.0119976301  0.0016046213  0.0033376123
## concep_2013    -0.006462921  0.0314834930 -0.0022464698 -0.0167736414
## maternal_age   -0.002069755  0.0029368513  0.0128775828 -0.0263135433
## any_smoker      0.003416609 -0.0007241368  0.0012836970 -0.0014548567
## smokeSH         0.011735953 -0.0051512458 -0.0093068036 -0.0005990586
## mean_cpss      -0.017623185  0.0102636126  0.0090765847 -0.0058688239
## mean_epsd       0.021537334 -0.0093232881 -0.0185691459  0.0210706139
## male            0.000666535 -0.0028471742 -0.0073812580 -0.0017115961
## gest_age_w     -0.018839063 -0.0120553886 -0.0012405281  0.0303791551
## days_to_peapod  0.003874497  0.0061840510 -0.0155863326 -0.0080939552
##                  concep_2010   concep_2011   concep_2012   concep_2013
## lat             0.0109529805 -0.0226544797  0.0015394008  0.0089319968
## lon             0.0028301792  0.0224924333 -0.0023870971 -0.0236248234
## lat_lon_int    -0.0080079439  0.0277455872 -0.0022154991 -0.0167729167
## latina_re      -0.0085908956 -0.0105082124  0.0134047596  0.0047480333
## black_re        0.0117705145  0.0155672953 -0.0118346993 -0.0152908068
## other_re       -0.0010269576 -0.0003423192 -0.0007702182  0.0022250749
## ed_no_hs        0.0008887133  0.0112570356 -0.0047398045 -0.0072084527
## ed_hs           0.0074454429 -0.0063970903  0.0062259307 -0.0070389388
## ed_aa           0.0028438827  0.0029887100 -0.0056680162 -0.0011586189
## ed_4yr          0.0011454528  0.0057799282 -0.0067937198  0.0001514104
## low_bmi         0.0024883974  0.0025081465 -0.0047990520 -0.0001579935
## ovwt_bmi       -0.0032388664  0.0065567295 -0.0054902735  0.0025081465
## obese_bmi      -0.0049965439  0.0026710773  0.0090401896 -0.0064629209
## concep_spring  -0.0233040387  0.0041308713 -0.0119976301  0.0314834930
## concep_summer   0.0012836970 -0.0003209243  0.0016046213 -0.0022464698
## concep_fall     0.0267008986 -0.0129225503  0.0033376123 -0.0167736414
## concep_2010     0.1407721931 -0.0497481979 -0.0475757875 -0.0432309667
## concep_2011    -0.0497481979  0.2076610381 -0.0825367829 -0.0749991771
## concep_2012    -0.0475757875 -0.0825367829  0.2021970969 -0.0717241039
## concep_2013    -0.0432309667 -0.0749991771 -0.0717241039  0.1902817550
## maternal_age   -0.0328905868 -0.0432339945  0.0317389331  0.0462084289
## any_smoker      0.0031993680  0.0090319608 -0.0078206774 -0.0042987393
## smokeSH         0.0094203614  0.0145535038 -0.0182136862 -0.0067262434
## mean_cpss       0.0079265785 -0.0141064917 -0.0086484999  0.0104679503
## mean_epsd      -0.0144672243  0.0406582459 -0.0297416911  0.0052396759
## male            0.0014811889 -0.0050936441  0.0014071295  0.0028554030
## gest_age_w     -0.0066182705 -0.0045846526  0.0012150814  0.0089551286
## days_to_peapod -0.0279586414 -0.0014177042 -0.0328007113  0.0624841560
##                maternal_age    any_smoker       smokeSH    mean_cpss
## lat             0.034857876 -0.0069992076  0.0011347413 -0.027918789
## lon            -0.193010308  0.0222429459  0.0442610839 -0.004658657
## lat_lon_int    -0.105532928  0.0146350446  0.0165959949  0.021381618
## latina_re      -0.111302369 -0.0075376057 -0.0034972516 -0.040327497
## black_re       -0.091496072  0.0150883776  0.0321961094 -0.036204440
## other_re       -0.013540656 -0.0006846384  0.0065896448  0.022573478
## ed_no_hs       -0.147331145  0.0173792831  0.0324874099 -0.057435615
## ed_hs          -0.106126638  0.0045357296  0.0251818571 -0.035645162
## ed_aa          -0.034152305  0.0085448142  0.0211184622  0.029189204
## ed_4yr          0.107777610 -0.0153977815 -0.0353773740  0.027517480
## low_bmi        -0.009197123  0.0011652019  0.0026463908  0.007997746
## ovwt_bmi        0.006732745 -0.0048582996 -0.0108818011 -0.004316432
## obese_bmi      -0.002069755  0.0034166091  0.0117359534 -0.017623185
## concep_spring   0.002936851 -0.0007241368 -0.0051512458  0.010263613
## concep_summer   0.012877583  0.0012836970 -0.0093068036  0.009076585
## concep_fall    -0.026313543 -0.0014548567 -0.0005990586 -0.005868824
## concep_2010    -0.032890587  0.0031993680  0.0094203614  0.007926578
## concep_2011    -0.043233995  0.0090319608  0.0145535038 -0.014106492
## concep_2012     0.031738933 -0.0078206774 -0.0182136862 -0.008648500
## concep_2013     0.046208429 -0.0042987393 -0.0067262434  0.010467950
## maternal_age    1.000000000 -0.0452178456 -0.1497337791  0.111663918
## any_smoker     -0.045217846  0.0796813798  0.0490043119  0.012438902
## smokeSH        -0.149733779  0.0490043119  0.1864504131  0.022013301
## mean_cpss       0.111663918  0.0124389018  0.0220133014  1.000000000
## mean_epsd      -0.170707705  0.0453127030  0.1111391210  0.441020650
## male            0.026063884  0.0020078338  0.0016210790 -0.007214721
## gest_age_w      0.073088144 -0.0297069373 -0.0509973685 -0.007275391
## days_to_peapod -0.001591990 -0.0022885196  0.0107316422 -0.005995421
##                   mean_epsd          male   gest_age_w days_to_peapod
## lat            -0.045887330  0.0224103855  0.030274459  0.01661775239
## lon             0.057378431 -0.0245595335 -0.083351848 -0.00375826760
## lat_lon_int     0.060923471 -0.0283648398 -0.058256588 -0.01529743598
## latina_re       0.039084315  0.0015223330 -0.007729444 -0.00006310256
## black_re        0.016092746 -0.0055544584 -0.045967398  0.03530798637
## other_re        0.021083961  0.0021394951 -0.005155083  0.00371884427
## ed_no_hs        0.071535296 -0.0151081268 -0.012119005  0.00689921335
## ed_hs           0.022143943  0.0007488233 -0.014831203  0.00147659993
## ed_aa           0.016391602  0.0011191205 -0.025824190  0.02524943813
## ed_4yr         -0.048192595  0.0062868240  0.033036218 -0.01071060804
## low_bmi         0.010783426 -0.0001974919 -0.003333522 -0.00737037914
## ovwt_bmi        0.009808061 -0.0029623778 -0.015929653 -0.01397511387
## obese_bmi       0.021537334  0.0006665350 -0.018839063  0.00387449725
## concep_spring  -0.009323288 -0.0028471742 -0.012055389  0.00618405099
## concep_summer  -0.018569146 -0.0073812580 -0.001240528 -0.01558633260
## concep_fall     0.021070614 -0.0017115961  0.030379155 -0.00809395517
## concep_2010    -0.014467224  0.0014811889 -0.006618270 -0.02795864142
## concep_2011     0.040658246 -0.0050936441 -0.004584653 -0.00141770421
## concep_2012    -0.029741691  0.0014071295  0.001215081 -0.03280071127
## concep_2013     0.005239676  0.0028554030  0.008955129  0.06248415603
## maternal_age   -0.170707705  0.0260638841  0.073088144 -0.00159199026
## any_smoker      0.045312703  0.0020078338 -0.029706937 -0.00228851955
## smokeSH         0.111139121  0.0016210790 -0.050997369  0.01073164223
## mean_cpss       0.441020650 -0.0072147212 -0.007275391 -0.00599542077
## mean_epsd       1.000000000 -0.0104804641 -0.086750438  0.01124930187
## male           -0.010480464  0.2502797801 -0.039081937  0.03073094727
## gest_age_w     -0.086750438 -0.0390819370  1.000000000 -0.13525838557
## days_to_peapod  0.011249302  0.0307309473 -0.135258386  1.00000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Response data: adiposty (%fat mass)

Y <- select(hs_data2, adiposity) %>%
  as.matrix()
head(Y)
##      adiposity
## [1,]  9.217429
## [2,]  7.736959
## [3,] 13.474442
## [4,] 10.058402
## [5,] 11.836774
## [6,] 15.544041

Distribution of adiposity and scaled adiposity

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

1.4 Scatterplots of exposures and outcome (adiposity)

Both adiposity (Y) and the exposures are scaled here

NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori

df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
  lm.x <- lm(adiposity ~ df[,x], data = df)
  plot(df[,c(x, 1)],
       xlab = paste0(colnames(df)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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2 Is gestational age a potenital mediator?

I.e., is there a relationship between our exposures and gestational age?

The DAG might look something like this:

exposures —> gestational age —> adiposity _________________________________^

2.1 Scatter plots for exposures and gestational age

Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery

Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.

df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
  lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
  plot(df2[,c(x, 1)],
       xlab = paste0(colnames(df2)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "gest_age_w"     "days_to_peapod"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled)-1)]
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"

3 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 28.18383
#' Fit the model using the best_lambda
ad_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(ad_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      20     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(ad_ridge)
## 21 x 1 sparse Matrix of class "dgCMatrix"
##                                    s0
## (Intercept)          9.70558400602256
## mean_pm             -0.02918998917658
## mean_o3             -0.00162273345759
## pct_tree_cover      -0.00707858012865
## pct_impervious      -0.00123913479050
## mean_aadt_intensity  0.00000009893812
## dist_m_tri           0.00000265205071
## dist_m_npl           0.00000212103152
## dist_m_waste_site    0.00001231150399
## dist_m_major_emit    0.00000345442313
## dist_m_cafo         -0.00000151278368
## dist_m_mine_well    -0.00000771268856
## cvd_rate_adj        -0.00040306658209
## res_rate_adj        -0.00083778715037
## violent_crime_rate  -0.00225734349381
## property_crime_rate -0.00082078900373
## pct_less_hs         -0.00020033888696
## pct_unemp           -0.00455074179190
## pct_limited_eng      0.00165523913246
## pct_hh_pov          -0.00198488819875
## pct_poc              0.00033884831986

Ridge regression predictions

ridge_pred <- predict(ad_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.01. Based on these results, it doesn’t look like there’s much here.

4 Nonparametric Bayesian Shrinkage (NPB): Adiposity

Still, we wanted to try to fit the NPB model with these data.

4.1 Finding the NPB priors

I’m starting with the sets of priors used in the birth weight analysis. Note: I’m including far fewer iterations of the priors than in the previous version of the document.

4.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]  -0.0002244638 0.03065891   0.00000000    0.0000000 0.022
##  [2,]  -0.0067958594 0.04315122  -0.11098145    0.0000000 0.040
##  [3,]  -0.0008083469 0.01719508   0.00000000    0.0000000 0.024
##  [4,]  -0.0017197218 0.01517309   0.00000000    0.0000000 0.016
##  [5,]   0.0028260054 0.03283555   0.00000000    0.0000000 0.020
##  [6,]  -0.0012387698 0.01700948   0.00000000    0.0000000 0.018
##  [7,]  -0.0022919297 0.02029178   0.00000000    0.0000000 0.024
##  [8,]   0.0120896780 0.07253021   0.00000000    0.2618768 0.046
##  [9,]  -0.0002699095 0.01684193   0.00000000    0.0000000 0.014
## [10,]  -0.0012055379 0.05334396  -0.02153362    0.0000000 0.030
## [11,]  -0.0038794699 0.02685319  -0.05108612    0.0000000 0.034
## [12,]  -0.0044363973 0.03007248  -0.07547669    0.0000000 0.036
## [13,]  -0.0047005066 0.02977325  -0.09291597    0.0000000 0.046
## [14,]  -0.0026175677 0.02044266   0.00000000    0.0000000 0.020
## [15,]  -0.0121813286 0.04984710  -0.19301230    0.0000000 0.072
## [16,]  -0.0029962666 0.02356645   0.00000000    0.0000000 0.028
## [17,]  -0.0050847531 0.02860052  -0.09098849    0.0000000 0.036
## [18,]  -0.0023298020 0.01995217  -0.03393439    0.0000000 0.034
## [19,]  -0.0052407963 0.03149169  -0.09802491    0.0000000 0.040
## [20,]  -0.0032854285 0.02067841  -0.04574963    0.0000000 0.028
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

4.1.2 Adjust alpha.pi and beta.pi

For now, leave a.phi1 and sig2inv.mu1 alone for now.

alpha.pi and beta.pi are responisble for the exclusion probability distribution. If we thing we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value

4.1.2.1 Try making alpha.pi and beta.pi 2

plot(density(rbeta(10000, 2, 2)))

priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]  -0.0008128463 0.03124739 -0.045426603   0.00000000 0.056
##  [2,]  -0.0109923737 0.05491148 -0.188489076   0.00000000 0.080
##  [3,]  -0.0012359181 0.02669459 -0.044244016   0.00000000 0.050
##  [4,]  -0.0016687622 0.02705344 -0.057107448   0.00000000 0.056
##  [5,]   0.0035674066 0.03439731  0.000000000   0.01238072 0.050
##  [6,]  -0.0045888455 0.02966178 -0.080787479   0.00000000 0.054
##  [7,]  -0.0014623699 0.01508674  0.000000000   0.00000000 0.032
##  [8,]   0.0128235902 0.07731286 -0.009077207   0.28821531 0.078
##  [9,]   0.0003622225 0.03485964 -0.033825431   0.00000000 0.052
## [10,]  -0.0069302298 0.06327613 -0.142188896   0.00000000 0.076
## [11,]  -0.0067992179 0.03816478 -0.125524049   0.00000000 0.074
## [12,]  -0.0066837066 0.04192488 -0.129441981   0.00000000 0.078
## [13,]  -0.0077043807 0.03757038 -0.122125837   0.00000000 0.072
## [14,]  -0.0054648574 0.03264103 -0.109504269   0.00000000 0.062
## [15,]  -0.0217930149 0.07215156 -0.271541695   0.00000000 0.132
## [16,]  -0.0071413917 0.03840063 -0.134233049   0.00000000 0.062
## [17,]  -0.0121014969 0.05691746 -0.162052752   0.00000000 0.072
## [18,]  -0.0008698144 0.02599417 -0.043015340   0.00000000 0.058
## [19,]  -0.0097883543 0.05050330 -0.133665258   0.00000000 0.074
## [20,]  -0.0011165392 0.02251249 -0.015092778   0.00000000 0.040
plot(fit.npb.12$beta[,1], type = "l")

plot(fit.npb.12$beta[,2], type = "l")

plot(fit.npb.12$beta[,13], type = "l")

4.1.2.2 Try making alpha.pi and beta.pi 5

plot(density(rbeta(10000, 5, 5)))

priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]  -0.0100391500 0.04058843  -0.13728609  0.013267286 0.174
##  [2,]  -0.0311859775 0.09213937  -0.26277390  0.015386575 0.292
##  [3,]  -0.0067509157 0.04136229  -0.14205888  0.038934495 0.190
##  [4,]  -0.0101389914 0.03955327  -0.14086250  0.027123622 0.204
##  [5,]  -0.0002972584 0.04043334  -0.07729877  0.064741092 0.170
##  [6,]  -0.0074013398 0.04128202  -0.13728609  0.033609749 0.174
##  [7,]  -0.0058340326 0.03155346  -0.11077735  0.020271451 0.166
##  [8,]   0.0179548429 0.09093975  -0.05469514  0.335231954 0.184
##  [9,]  -0.0037851039 0.02545463  -0.08254335  0.022396935 0.130
## [10,]  -0.0175285140 0.06858538  -0.21628723  0.029974338 0.252
## [11,]  -0.0250479003 0.07014295  -0.23944156  0.020271451 0.266
## [12,]  -0.0195000190 0.05692325  -0.18818772  0.006343339 0.238
## [13,]  -0.0201877423 0.05403820  -0.20158552  0.006218584 0.240
## [14,]  -0.0128061241 0.04761605  -0.16126539  0.011007052 0.204
## [15,]  -0.0461864279 0.08968315  -0.29500794  0.001394794 0.360
## [16,]  -0.0188574365 0.05846165  -0.20019070  0.001778855 0.230
## [17,]  -0.0295499716 0.08043544  -0.28515681  0.000000000 0.246
## [18,]  -0.0061240400 0.03870974  -0.10508979  0.007924296 0.174
## [19,]  -0.0149240850 0.04859332  -0.17037055  0.015386575 0.222
## [20,]  -0.0056698357 0.04565578  -0.12725984  0.030992398 0.180
plot(fit.npb.13$beta[,1], type = "l")

plot(fit.npb.13$beta[,2], type = "l")

plot(fit.npb.13$beta[,13], type = "l")

4.1.2.3 Try making alpha.pi and beta.pi 8

plot(density(rbeta(10000, 8, 8)))

priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]  -0.0157696404 0.05447552  -0.15739908   0.04315442 0.276
##  [2,]  -0.0295029568 0.07686046  -0.24874160   0.08394220 0.396
##  [3,]  -0.0121124911 0.05220660  -0.14452240   0.05045757 0.256
##  [4,]  -0.0166617178 0.05371270  -0.16163881   0.02241358 0.242
##  [5,]   0.0052419830 0.05321659  -0.08229548   0.16517177 0.194
##  [6,]  -0.0171402228 0.05459742  -0.15161805   0.03931312 0.252
##  [7,]  -0.0057918603 0.03381693  -0.10635877   0.04204706 0.192
##  [8,]   0.0263437385 0.10106607  -0.06271938   0.37720331 0.236
##  [9,]   0.0001177643 0.04926960  -0.09959640   0.13982299 0.194
## [10,]  -0.0127356580 0.09023425  -0.22158768   0.14588132 0.308
## [11,]  -0.0350484822 0.07639394  -0.25187356   0.01714852 0.352
## [12,]  -0.0179969693 0.05881989  -0.19021602   0.04022551 0.290
## [13,]  -0.0283373799 0.06755326  -0.24525294   0.01712042 0.326
## [14,]  -0.0114105676 0.07067475  -0.15015841   0.07270539 0.296
## [15,]  -0.0670070386 0.11688415  -0.38054144   0.00000000 0.456
## [16,]  -0.0253082592 0.09129863  -0.24399241   0.04609970 0.300
## [17,]  -0.0398855660 0.08887281  -0.31011867   0.01740361 0.360
## [18,]  -0.0045569685 0.05756825  -0.12005709   0.09556167 0.256
## [19,]  -0.0260463966 0.06471700  -0.19534249   0.00000000 0.290
## [20,]  -0.0077528761 0.05531862  -0.12638982   0.03686140 0.226
plot(fit.npb.14$beta[,1], type = "l")

plot(fit.npb.14$beta[,2], type = "l")

plot(fit.npb.14$beta[,13], type = "l")

4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1

Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1

4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1

priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 1)

fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.010776076 0.05349721  -0.15983725   0.07186679 0.272
##  [2,]   -0.023840033 0.08083899  -0.22343347   0.06865878 0.316
##  [3,]   -0.006297729 0.05256468  -0.14040269   0.11545590 0.268
##  [4,]   -0.008872432 0.04551965  -0.14155830   0.08393444 0.238
##  [5,]    0.005228278 0.05885120  -0.07828619   0.13906800 0.230
##  [6,]   -0.011272841 0.05409252  -0.16617134   0.08191122 0.264
##  [7,]   -0.004263896 0.04741990  -0.12623117   0.11406338 0.216
##  [8,]    0.024492471 0.09102470  -0.07647902   0.29000886 0.272
##  [9,]    0.001442495 0.04810147  -0.09193480   0.10594137 0.214
## [10,]   -0.023658106 0.13556533  -0.27858483   0.09359547 0.340
## [11,]   -0.026124365 0.07440119  -0.24393261   0.05356252 0.334
## [12,]   -0.021586576 0.05904021  -0.18693920   0.04710151 0.326
## [13,]   -0.025288324 0.06889897  -0.21201483   0.03397377 0.302
## [14,]   -0.011316598 0.05236428  -0.16085115   0.06053328 0.242
## [15,]   -0.062182020 0.10466476  -0.36330743   0.00659731 0.450
## [16,]   -0.016349837 0.05699490  -0.19670489   0.06822506 0.258
## [17,]   -0.040071602 0.09331811  -0.35274180   0.03896274 0.354
## [18,]   -0.004190913 0.05497043  -0.13770796   0.11981376 0.234
## [19,]   -0.022784679 0.06929598  -0.22197851   0.05161263 0.294
## [20,]   -0.008090274 0.05739451  -0.16064309   0.05268181 0.214
plot(fit.npb.23$beta[,1], type = "l")

plot(fit.npb.23$beta[,2], type = "l")

plot(fit.npb.23$beta[,13], type = "l")

4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.009324775 0.05481546  -0.15870289   0.07171425 0.272
##  [2,]   -0.035583946 0.09421746  -0.31208158   0.04528158 0.350
##  [3,]   -0.007146591 0.04943767  -0.14444216   0.06060265 0.248
##  [4,]   -0.015610240 0.05471313  -0.17028088   0.04364996 0.262
##  [5,]    0.012446920 0.06739039  -0.07168868   0.23653155 0.250
##  [6,]   -0.007264592 0.05030023  -0.12902314   0.09232996 0.276
##  [7,]   -0.003154088 0.05249611  -0.10978735   0.10618214 0.242
##  [8,]    0.042408726 0.11367189  -0.07477517   0.38840638 0.330
##  [9,]    0.003285676 0.04793397  -0.08662208   0.14483082 0.232
## [10,]   -0.017012527 0.11174794  -0.21958051   0.22669031 0.332
## [11,]   -0.033230221 0.08430399  -0.29177495   0.06087094 0.366
## [12,]   -0.025971443 0.06970725  -0.23669704   0.04451830 0.330
## [13,]   -0.030943847 0.08218177  -0.29875486   0.04360241 0.322
## [14,]   -0.008967903 0.05721818  -0.13945038   0.10916408 0.274
## [15,]   -0.064553616 0.10748442  -0.36395187   0.00000000 0.440
## [16,]   -0.016568711 0.05996401  -0.17755417   0.05133096 0.272
## [17,]   -0.040174596 0.09055339  -0.30403167   0.01090636 0.352
## [18,]   -0.002386577 0.05535941  -0.11369403   0.12042576 0.226
## [19,]   -0.035366803 0.09786180  -0.28907058   0.05309944 0.356
## [20,]   -0.002455106 0.05923952  -0.12332655   0.12806381 0.266
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

plot(fit.npb.24$beta[,15], type = "l")

4.2 Fit the NPB model

As with the birth weight model, I’ve used the 24th set of priors and set scaleY = T in the NPB model below

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "pct_tree_cover"     
##  [4] "pct_impervious"      "mean_aadt_intensity" "dist_m_tri"         
##  [7] "dist_m_npl"          "dist_m_waste_site"   "dist_m_major_emit"  
## [10] "dist_m_cafo"         "dist_m_mine_well"    "cvd_rate_adj"       
## [13] "res_rate_adj"        "violent_crime_rate"  "property_crime_rate"
## [16] "pct_less_hs"         "pct_unemp"           "pct_limited_eng"    
## [19] "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"
# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Adiposity_v3.rdata"))

load(here::here("Results", "NPB_Adiposity_v3.rdata"))
npb.sum <- summary(fit.npb)

4.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum$main.effects) <- colnames(X.scaled)
npb.sum$main.effects
##                     Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
## mean_pm               -0.009521478 0.05821512  -0.15830691   0.10684002 0.3116
## mean_o3               -0.030065414 0.08499379  -0.28834910   0.06087740 0.3612
## pct_tree_cover        -0.006925560 0.05544297  -0.14394429   0.09929996 0.2824
## pct_impervious        -0.011747909 0.05126717  -0.14572875   0.06744699 0.2900
## mean_aadt_intensity    0.007088029 0.05965890  -0.08273797   0.18528231 0.2648
## dist_m_tri            -0.010895546 0.05857536  -0.16787708   0.09608965 0.3036
## dist_m_npl            -0.002794456 0.04977971  -0.11776067   0.10745454 0.2628
## dist_m_waste_site      0.033156529 0.10837580  -0.07790025   0.39905857 0.3172
## dist_m_major_emit      0.001631657 0.05553538  -0.10690768   0.14252991 0.2584
## dist_m_cafo           -0.015783270 0.11410095  -0.24385825   0.15703486 0.3328
## dist_m_mine_well      -0.027086077 0.07251168  -0.23691818   0.06002946 0.3652
## cvd_rate_adj          -0.020069284 0.06390855  -0.19854017   0.05690473 0.3148
## res_rate_adj          -0.024984788 0.06857139  -0.22057351   0.04218614 0.3408
## violent_crime_rate    -0.015349772 0.05718232  -0.17417776   0.05789069 0.3024
## property_crime_rate   -0.064508052 0.11463374  -0.39703779   0.02707757 0.4808
## pct_less_hs           -0.018611264 0.06656410  -0.19998674   0.06008295 0.3160
## pct_unemp             -0.039610700 0.09020572  -0.32858144   0.02475102 0.3800
## pct_limited_eng        0.001481397 0.06073486  -0.10731547   0.15831849 0.2664
## pct_hh_pov            -0.027219328 0.07633254  -0.24312458   0.04018555 0.3424
## pct_poc               -0.002740457 0.05712510  -0.12356143   0.13039102 0.2772
npb.sum$main.effects$exp <- rownames(npb.sum$main.effects)
## Warning in npb.sum$main.effects$exp <- rownames(npb.sum$main.effects): Coercing
## LHS to a list
write_csv(as.data.frame(npb.sum$main.effects), here::here("Results", "NPB_Main_Effects_Adiposity.csv"))

#' Which one's have PIPs > 0.5
# selected_exp <- which(npb.sum$main.effects[,5] >= 0.5)
# selected_exp

4.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum$interactions
##         Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  0.000714816335 0.018705637  0.000000000            0 0.0060
##   [2,] -0.000709420029 0.010064647  0.000000000            0 0.0080
##   [3,] -0.002678101635 0.023422750  0.000000000            0 0.0180
##   [4,] -0.000302982235 0.005240192  0.000000000            0 0.0056
##   [5,] -0.000567884373 0.009659061  0.000000000            0 0.0092
##   [6,] -0.000487813821 0.007500479  0.000000000            0 0.0064
##   [7,] -0.004171511437 0.029329812 -0.035988587            0 0.0268
##   [8,] -0.002289342406 0.022176267  0.000000000            0 0.0160
##   [9,] -0.001285642778 0.015935178  0.000000000            0 0.0104
##  [10,] -0.001332104520 0.014898732  0.000000000            0 0.0120
##  [11,] -0.001204675266 0.014287677  0.000000000            0 0.0120
##  [12,] -0.000354660216 0.008338736  0.000000000            0 0.0064
##  [13,] -0.000434038738 0.006454505  0.000000000            0 0.0064
##  [14,] -0.000122558194 0.005132664  0.000000000            0 0.0064
##  [15,] -0.001841345005 0.017656567  0.000000000            0 0.0164
##  [16,] -0.002144475243 0.020332125  0.000000000            0 0.0156
##  [17,] -0.003182674834 0.027740483  0.000000000            0 0.0204
##  [18,] -0.000553766044 0.008478782  0.000000000            0 0.0080
##  [19,] -0.001668649713 0.017562827  0.000000000            0 0.0136
##  [20,] -0.000445826172 0.007132295  0.000000000            0 0.0056
##  [21,] -0.000249481048 0.006420783  0.000000000            0 0.0060
##  [22,]  0.000181260526 0.010773276  0.000000000            0 0.0060
##  [23,] -0.002138987498 0.019864111  0.000000000            0 0.0176
##  [24,] -0.000827733741 0.010805316  0.000000000            0 0.0084
##  [25,] -0.000737277930 0.010393739  0.000000000            0 0.0108
##  [26,] -0.000413700815 0.006759402  0.000000000            0 0.0068
##  [27,] -0.000583993114 0.006950099  0.000000000            0 0.0092
##  [28,] -0.000864117404 0.010449808  0.000000000            0 0.0112
##  [29,] -0.000066503782 0.005968716  0.000000000            0 0.0048
##  [30,] -0.000170163209 0.004318929  0.000000000            0 0.0052
##  [31,] -0.000189453818 0.003991600  0.000000000            0 0.0048
##  [32,] -0.000364989861 0.006150400  0.000000000            0 0.0060
##  [33,] -0.001041262057 0.012940966  0.000000000            0 0.0112
##  [34,] -0.000471552169 0.008887122  0.000000000            0 0.0084
##  [35,] -0.000348259672 0.006357364  0.000000000            0 0.0048
##  [36,] -0.000214270045 0.004322548  0.000000000            0 0.0040
##  [37,] -0.001883444729 0.017048341  0.000000000            0 0.0156
##  [38,] -0.000371678917 0.006050061  0.000000000            0 0.0056
##  [39,] -0.000119103273 0.008205004  0.000000000            0 0.0056
##  [40,] -0.000229014558 0.003888444  0.000000000            0 0.0048
##  [41,] -0.000252044262 0.006048754  0.000000000            0 0.0044
##  [42,] -0.000223354995 0.005612090  0.000000000            0 0.0052
##  [43,]  0.000212518611 0.010866769  0.000000000            0 0.0076
##  [44,] -0.001279899659 0.015969309  0.000000000            0 0.0100
##  [45,] -0.000803264264 0.011559414  0.000000000            0 0.0092
##  [46,] -0.000367945543 0.007009637  0.000000000            0 0.0052
##  [47,] -0.000536520982 0.008730588  0.000000000            0 0.0056
##  [48,] -0.000712399238 0.009685180  0.000000000            0 0.0080
##  [49,] -0.000161425498 0.007772472  0.000000000            0 0.0040
##  [50,] -0.001090586982 0.015252794  0.000000000            0 0.0108
##  [51,] -0.000756738730 0.012137244  0.000000000            0 0.0080
##  [52,] -0.000701395263 0.010527526  0.000000000            0 0.0080
##  [53,] -0.000542225668 0.008111342  0.000000000            0 0.0064
##  [54,] -0.000853230359 0.011073983  0.000000000            0 0.0096
##  [55,]  0.000136226048 0.007197069  0.000000000            0 0.0056
##  [56,] -0.000036605044 0.001851556  0.000000000            0 0.0020
##  [57,] -0.000117341855 0.003826224  0.000000000            0 0.0036
##  [58,] -0.000165992032 0.003111426  0.000000000            0 0.0040
##  [59,] -0.000289220494 0.006124989  0.000000000            0 0.0044
##  [60,] -0.000164722849 0.003348375  0.000000000            0 0.0044
##  [61,] -0.000766508478 0.010960191  0.000000000            0 0.0088
##  [62,] -0.001718436446 0.016793540  0.000000000            0 0.0156
##  [63,] -0.002625839237 0.020711075  0.000000000            0 0.0220
##  [64,] -0.000301717388 0.005893842  0.000000000            0 0.0048
##  [65,] -0.000288801444 0.006120300  0.000000000            0 0.0032
##  [66,] -0.001078473377 0.015974588  0.000000000            0 0.0088
##  [67,] -0.000821040959 0.010450675  0.000000000            0 0.0088
##  [68,] -0.000330429359 0.006521981  0.000000000            0 0.0072
##  [69,] -0.000642019537 0.011290758  0.000000000            0 0.0068
##  [70,] -0.000902827328 0.011160465  0.000000000            0 0.0112
##  [71,] -0.000224610529 0.005336016  0.000000000            0 0.0044
##  [72,] -0.000234167796 0.004596488  0.000000000            0 0.0052
##  [73,] -0.000347742507 0.005700044  0.000000000            0 0.0068
##  [74,] -0.001117111575 0.012727464  0.000000000            0 0.0132
##  [75,] -0.000098440507 0.006042556  0.000000000            0 0.0032
##  [76,] -0.000446199104 0.007007022  0.000000000            0 0.0064
##  [77,] -0.001482612420 0.015225070  0.000000000            0 0.0132
##  [78,] -0.001284512717 0.014848840  0.000000000            0 0.0140
##  [79,] -0.000615931247 0.008570273  0.000000000            0 0.0080
##  [80,] -0.000127166918 0.003179602  0.000000000            0 0.0044
##  [81,] -0.002185942536 0.020854941  0.000000000            0 0.0160
##  [82,] -0.001084340750 0.013267686  0.000000000            0 0.0120
##  [83,] -0.000722310845 0.010040989  0.000000000            0 0.0108
##  [84,] -0.000388306893 0.008518620  0.000000000            0 0.0056
##  [85,] -0.001152113624 0.012959401  0.000000000            0 0.0116
##  [86,] -0.000682118135 0.008220938  0.000000000            0 0.0092
##  [87,] -0.000465271634 0.008757902  0.000000000            0 0.0064
##  [88,] -0.000512441694 0.008106343  0.000000000            0 0.0068
##  [89,] -0.000100051884 0.011743763  0.000000000            0 0.0072
##  [90,] -0.000747459521 0.010487885  0.000000000            0 0.0092
##  [91,] -0.000341812306 0.005907964  0.000000000            0 0.0060
##  [92,] -0.000168864218 0.004973623  0.000000000            0 0.0052
##  [93,] -0.000947873278 0.011288244  0.000000000            0 0.0108
##  [94,] -0.000440398838 0.006389300  0.000000000            0 0.0060
##  [95,] -0.000270047624 0.007404247  0.000000000            0 0.0084
##  [96,] -0.000017042871 0.008021645  0.000000000            0 0.0040
##  [97,] -0.000402069858 0.008571568  0.000000000            0 0.0064
##  [98,] -0.000136166508 0.005081306  0.000000000            0 0.0060
##  [99,] -0.000277730555 0.007474456  0.000000000            0 0.0056
## [100,] -0.000365920504 0.008473786  0.000000000            0 0.0064
## [101,] -0.000937631525 0.012019211  0.000000000            0 0.0096
## [102,]  0.000010092457 0.004091005  0.000000000            0 0.0044
## [103,] -0.000411109539 0.007889720  0.000000000            0 0.0060
## [104,]  0.000080448078 0.014865502  0.000000000            0 0.0068
## [105,]  0.000038255372 0.003813115  0.000000000            0 0.0040
## [106,] -0.000686936024 0.009652154  0.000000000            0 0.0076
## [107,] -0.000460702807 0.006976554  0.000000000            0 0.0072
## [108,] -0.000638952486 0.008805782  0.000000000            0 0.0100
## [109,] -0.000172205494 0.004855775  0.000000000            0 0.0056
## [110,] -0.001067885006 0.013742504  0.000000000            0 0.0120
## [111,] -0.000229793972 0.012766673  0.000000000            0 0.0068
## [112,] -0.000527134558 0.008361285  0.000000000            0 0.0092
## [113,] -0.000351229481 0.007729758  0.000000000            0 0.0060
## [114,]  0.000314182448 0.018075507  0.000000000            0 0.0072
## [115,] -0.000504240379 0.008434012  0.000000000            0 0.0068
## [116,] -0.000786987710 0.012157232  0.000000000            0 0.0072
## [117,] -0.000601924434 0.011582185  0.000000000            0 0.0084
## [118,] -0.001197512024 0.015884501  0.000000000            0 0.0092
## [119,] -0.000554558311 0.008030672  0.000000000            0 0.0084
## [120,] -0.001233643793 0.014759603  0.000000000            0 0.0112
## [121,] -0.000282710293 0.007139287  0.000000000            0 0.0084
## [122,] -0.000429959742 0.008504538  0.000000000            0 0.0076
## [123,] -0.000437792991 0.009828900  0.000000000            0 0.0108
## [124,] -0.000930862644 0.012303130  0.000000000            0 0.0112
## [125,]  0.000526310070 0.012503653  0.000000000            0 0.0064
## [126,]  0.000068623944 0.012719470  0.000000000            0 0.0048
## [127,] -0.000650757399 0.009324578  0.000000000            0 0.0072
## [128,] -0.000279511893 0.006051769  0.000000000            0 0.0048
## [129,] -0.001010040846 0.011170269  0.000000000            0 0.0124
## [130,] -0.000218746726 0.007139723  0.000000000            0 0.0044
## [131,] -0.002831449520 0.021999127  0.000000000            0 0.0216
## [132,] -0.002482934644 0.018742850  0.000000000            0 0.0232
## [133,] -0.001022415422 0.012837211  0.000000000            0 0.0108
## [134,] -0.000603688106 0.008332915  0.000000000            0 0.0092
## [135,] -0.001568585278 0.017109643  0.000000000            0 0.0140
## [136,] -0.000738051759 0.009556530  0.000000000            0 0.0100
## [137,] -0.000665878570 0.009588982  0.000000000            0 0.0084
## [138,] -0.000413278204 0.008729327  0.000000000            0 0.0072
## [139,] -0.000582616698 0.007439775  0.000000000            0 0.0092
## [140,] -0.000107892367 0.003193256  0.000000000            0 0.0044
## [141,] -0.000574116189 0.009286238  0.000000000            0 0.0048
## [142,] -0.000395370270 0.011628401  0.000000000            0 0.0076
## [143,] -0.000280980933 0.009394016  0.000000000            0 0.0064
## [144,] -0.000694273879 0.013963990  0.000000000            0 0.0064
## [145,] -0.000527644750 0.010902194  0.000000000            0 0.0080
## [146,] -0.000362266307 0.005551096  0.000000000            0 0.0056
## [147,]  0.000148133306 0.011812362  0.000000000            0 0.0064
## [148,] -0.000213652221 0.003378633  0.000000000            0 0.0048
## [149,] -0.000087222894 0.005002666  0.000000000            0 0.0028
## [150,] -0.000374150662 0.006012979  0.000000000            0 0.0052
## [151,]  0.000304400213 0.013468017  0.000000000            0 0.0056
## [152,] -0.000513085000 0.007580655  0.000000000            0 0.0064
## [153,] -0.000121246266 0.006478759  0.000000000            0 0.0064
## [154,] -0.000530006469 0.007523285  0.000000000            0 0.0088
## [155,] -0.004045015871 0.026873564 -0.047192386            0 0.0288
## [156,] -0.000393136137 0.008954958  0.000000000            0 0.0048
## [157,] -0.000325503161 0.006441203  0.000000000            0 0.0044
## [158,] -0.001688693060 0.017493598  0.000000000            0 0.0136
## [159,] -0.006875607702 0.043271258 -0.113287884            0 0.0352
## [160,] -0.000405110893 0.005662103  0.000000000            0 0.0088
## [161,] -0.001206908481 0.014890590  0.000000000            0 0.0100
## [162,] -0.001631626748 0.017119550  0.000000000            0 0.0132
## [163,] -0.000175970229 0.004729006  0.000000000            0 0.0036
## [164,] -0.000343197913 0.006034807  0.000000000            0 0.0052
## [165,] -0.000852538592 0.010177179  0.000000000            0 0.0112
## [166,] -0.000965930971 0.011207925  0.000000000            0 0.0120
## [167,] -0.000563731270 0.008193031  0.000000000            0 0.0064
## [168,] -0.000689276246 0.009539027  0.000000000            0 0.0100
## [169,] -0.000953386787 0.014612838  0.000000000            0 0.0092
## [170,] -0.000086815454 0.002371249  0.000000000            0 0.0028
## [171,]  0.000030292271 0.003660468  0.000000000            0 0.0056
## [172,] -0.000188778584 0.005657771  0.000000000            0 0.0036
## [173,] -0.000008758806 0.003947744  0.000000000            0 0.0040
## [174,] -0.000104265972 0.003496444  0.000000000            0 0.0048
## [175,] -0.000266465736 0.007079068  0.000000000            0 0.0060
## [176,] -0.000004662324 0.006470991  0.000000000            0 0.0040
## [177,]  0.000161758494 0.009505010  0.000000000            0 0.0068
## [178,]  0.000205408110 0.009065347  0.000000000            0 0.0040
## [179,] -0.000318666721 0.007623910  0.000000000            0 0.0056
## [180,] -0.000173887648 0.007123707  0.000000000            0 0.0036
## [181,] -0.000771467861 0.008699319  0.000000000            0 0.0112
## [182,] -0.000275287638 0.005125504  0.000000000            0 0.0036
## [183,] -0.000565991963 0.008396880  0.000000000            0 0.0100
## [184,] -0.000631506187 0.009952924  0.000000000            0 0.0080
## [185,] -0.000337235562 0.005760513  0.000000000            0 0.0052
## [186,] -0.000170379850 0.005979503  0.000000000            0 0.0040
## [187,] -0.001009193885 0.011042949  0.000000000            0 0.0116
## [188,] -0.000193918488 0.005208199  0.000000000            0 0.0036
## [189,] -0.000484665203 0.007220311  0.000000000            0 0.0076
## [190,] -0.000618306529 0.009372844  0.000000000            0 0.0080
## [191,] -0.000167509415 0.003178525  0.000000000            0 0.0040
## [192,] -0.000420428724 0.008176756  0.000000000            0 0.0068
## [193,] -0.001819705393 0.017693085  0.000000000            0 0.0168
## [194,] -0.000664864441 0.010403659  0.000000000            0 0.0060
## [195,] -0.000674321004 0.011450233  0.000000000            0 0.0100
## [196,] -0.001039070832 0.011690880  0.000000000            0 0.0104
## [197,] -0.000145806522 0.005691066  0.000000000            0 0.0032
## [198,] -0.000767588741 0.010383474  0.000000000            0 0.0092
## [199,] -0.002726473286 0.029246404  0.000000000            0 0.0172
## [200,] -0.000477623659 0.012315340  0.000000000            0 0.0076
## [201,] -0.001423852853 0.020633044  0.000000000            0 0.0100
## [202,] -0.003907970556 0.035130197  0.000000000            0 0.0196
## [203,] -0.000515933421 0.009041328  0.000000000            0 0.0048
## [204,]  0.000127275091 0.021308806  0.000000000            0 0.0052
## [205,] -0.001575726128 0.022528848  0.000000000            0 0.0132
## [206,] -0.002188078851 0.020076332  0.000000000            0 0.0168
## [207,] -0.001471239936 0.017651712  0.000000000            0 0.0140
## [208,] -0.000625921488 0.009495570  0.000000000            0 0.0072
## [209,] -0.000919941713 0.012710841  0.000000000            0 0.0084
## [210,] -0.001533572370 0.020444395  0.000000000            0 0.0120
## [211,] -0.002117837372 0.019333219  0.000000000            0 0.0168
## [212,] -0.000854084963 0.014175508  0.000000000            0 0.0068
## [213,] -0.001159898773 0.016420376  0.000000000            0 0.0112
## [214,] -0.000181776097 0.003396616  0.000000000            0 0.0052
## [215,] -0.000159650981 0.005254631  0.000000000            0 0.0044
## [216,] -0.000672451610 0.012241779  0.000000000            0 0.0092
## [217,] -0.000923938425 0.011069591  0.000000000            0 0.0100
## [218,] -0.000067528947 0.007326034  0.000000000            0 0.0048
## [219,] -0.002992904595 0.022849656  0.000000000            0 0.0208
## [220,] -0.005249454384 0.033285551 -0.083747446            0 0.0316
## [221,] -0.001013272847 0.013516399  0.000000000            0 0.0108
## [222,] -0.001465570817 0.017883633  0.000000000            0 0.0112
## [223,] -0.001290988471 0.014446362  0.000000000            0 0.0116
## [224,] -0.001077447248 0.018836106  0.000000000            0 0.0128
## [225,] -0.001068025661 0.014738778  0.000000000            0 0.0100
## [226,] -0.002507139089 0.025393049  0.000000000            0 0.0176
## [227,] -0.000258222723 0.015938055  0.000000000            0 0.0064
## [228,] -0.000585228488 0.010727579  0.000000000            0 0.0084
## [229,]  0.000147087643 0.010123464  0.000000000            0 0.0052
## [230,] -0.002704841612 0.026671700  0.000000000            0 0.0176
## [231,] -0.013061126153 0.113873178 -0.054813938            0 0.0316
## [232,] -0.000319434477 0.018886060  0.000000000            0 0.0100
## [233,] -0.000459473102 0.023889580  0.000000000            0 0.0096
## [234,] -0.002913566587 0.029956064  0.000000000            0 0.0172
## [235,] -0.000718152196 0.010896219  0.000000000            0 0.0076
## [236,] -0.000290986783 0.017743390  0.000000000            0 0.0084
## [237,]  0.000007992333 0.009643946  0.000000000            0 0.0056
## [238,] -0.000046761678 0.005479214  0.000000000            0 0.0056
## [239,] -0.001308781514 0.017911282  0.000000000            0 0.0100
## [240,] -0.003534457691 0.030620902  0.000000000            0 0.0200
## [241,] -0.000016724794 0.007424296  0.000000000            0 0.0056
## [242,] -0.000468041070 0.007807743  0.000000000            0 0.0088
## [243,] -0.002165411485 0.022007364  0.000000000            0 0.0128
## [244,] -0.000672463349 0.008353697  0.000000000            0 0.0080
## [245,] -0.000814437843 0.011531159  0.000000000            0 0.0084
## [246,] -0.000600776648 0.010387385  0.000000000            0 0.0052
## [247,] -0.000495281256 0.009998457  0.000000000            0 0.0040
## [248,] -0.000620016557 0.008211407  0.000000000            0 0.0088
## [249,] -0.000453030400 0.013459733  0.000000000            0 0.0084
## [250,] -0.000754386967 0.014256995  0.000000000            0 0.0108
## [251,] -0.001190892339 0.014754751  0.000000000            0 0.0104
## [252,] -0.000993374646 0.017785972  0.000000000            0 0.0112
## [253,] -0.000671478881 0.011738752  0.000000000            0 0.0092
## [254,] -0.000800957625 0.010854336  0.000000000            0 0.0088
## [255,] -0.001070691577 0.013919338  0.000000000            0 0.0108
## [256,] -0.000629579135 0.009836124  0.000000000            0 0.0084
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## [516,] -0.000983372393 0.012177785  0.000000000            0 0.0104
## [517,] -0.000918398853 0.012264914  0.000000000            0 0.0080
## [518,] -0.001356582639 0.016285268  0.000000000            0 0.0120
## [519,]  0.000046604082 0.019817195  0.000000000            0 0.0084
## [520,] -0.001857592717 0.020126187  0.000000000            0 0.0140
## [521,] -0.000957148481 0.015001636  0.000000000            0 0.0092
## [522,] -0.000891198247 0.014796065  0.000000000            0 0.0116
## [523,] -0.000269321764 0.007219464  0.000000000            0 0.0060
## [524,] -0.001448448030 0.016103258  0.000000000            0 0.0140
## [525,] -0.000915624409 0.019604555  0.000000000            0 0.0104
## [526,]  0.000808175194 0.031219703  0.000000000            0 0.0072
## [527,] -0.000660617676 0.010463948  0.000000000            0 0.0084
## [528,] -0.000686119626 0.010175204  0.000000000            0 0.0092
## [529,] -0.001523789120 0.016986684  0.000000000            0 0.0140
## [530,] -0.001485354852 0.015769905  0.000000000            0 0.0124
## [531,] -0.000987270047 0.013072526  0.000000000            0 0.0096
## [532,] -0.001251795235 0.014689000  0.000000000            0 0.0124
## [533,] -0.000730398223 0.011304242  0.000000000            0 0.0072
## [534,] -0.001016986292 0.012728136  0.000000000            0 0.0096
## [535,] -0.000686581130 0.011295817  0.000000000            0 0.0076
## [536,] -0.000782249307 0.010329232  0.000000000            0 0.0108
## [537,] -0.000883711590 0.012869558  0.000000000            0 0.0080
## [538,] -0.000479904653 0.010472011  0.000000000            0 0.0080
## [539,] -0.000668959213 0.009021401  0.000000000            0 0.0080
## [540,] -0.000973703098 0.013143281  0.000000000            0 0.0084
## [541,] -0.004249756961 0.038505189  0.000000000            0 0.0220
## [542,] -0.000499637462 0.007183133  0.000000000            0 0.0080
## [543,] -0.005186008556 0.033906247 -0.073124727            0 0.0320
## [544,] -0.001687583945 0.021582268  0.000000000            0 0.0136
## [545,] -0.000803995070 0.014431549  0.000000000            0 0.0088
## [546,] -0.000791195617 0.011747646  0.000000000            0 0.0076
## [547,] -0.001241635578 0.016312083  0.000000000            0 0.0088
## [548,] -0.000798169521 0.022085023  0.000000000            0 0.0064
## [549,]  0.000113122847 0.015794752  0.000000000            0 0.0060
## [550,] -0.000734651719 0.010725465  0.000000000            0 0.0068
## [551,] -0.002364746707 0.022865513  0.000000000            0 0.0180
## [552,] -0.001469129548 0.035937711  0.000000000            0 0.0108
## [553,] -0.000441956786 0.008763541  0.000000000            0 0.0092
## [554,] -0.000377674857 0.014158906  0.000000000            0 0.0076
## [555,] -0.001708676917 0.018910541  0.000000000            0 0.0124
## [556,] -0.001211932157 0.013578869  0.000000000            0 0.0144
## [557,] -0.000438830179 0.012269950  0.000000000            0 0.0064
## [558,] -0.001455973783 0.016476782  0.000000000            0 0.0120
## [559,] -0.002240111525 0.026441187  0.000000000            0 0.0148
## [560,] -0.000175327168 0.003561263  0.000000000            0 0.0036
## [561,] -0.001097271610 0.014041324  0.000000000            0 0.0096
## [562,] -0.000471380298 0.007199617  0.000000000            0 0.0072
## [563,] -0.001125779961 0.014023451  0.000000000            0 0.0120
## [564,] -0.000459785349 0.009114354  0.000000000            0 0.0060
## [565,] -0.001451227117 0.013978243  0.000000000            0 0.0144
## [566,] -0.002288715240 0.020953557  0.000000000            0 0.0184
## [567,] -0.001806797159 0.017706066  0.000000000            0 0.0136
## [568,] -0.002213100858 0.021901585  0.000000000            0 0.0152
## [569,] -0.000445361013 0.007467856  0.000000000            0 0.0060
## [570,] -0.000744776820 0.009317563  0.000000000            0 0.0092
## [571,] -0.000930226240 0.012359569  0.000000000            0 0.0104
## [572,] -0.001645484785 0.020943223  0.000000000            0 0.0148
## [573,] -0.001243829655 0.019413424  0.000000000            0 0.0116
## [574,] -0.005111630135 0.114686809  0.000000000            0 0.0148
## [575,] -0.001142057164 0.021490281  0.000000000            0 0.0096
## [576,] -0.000780060133 0.013014171  0.000000000            0 0.0076
## [577,] -0.000974187681 0.012514776  0.000000000            0 0.0120
## [578,] -0.002196324322 0.020629846  0.000000000            0 0.0164
## [579,] -0.001363632722 0.016840550  0.000000000            0 0.0148
## [580,] -0.001032274629 0.012663901  0.000000000            0 0.0116
## [581,] -0.001178954581 0.013316938  0.000000000            0 0.0108
## [582,] -0.001669572436 0.020255766  0.000000000            0 0.0124
## [583,] -0.002320312415 0.023737427  0.000000000            0 0.0152
## [584,] -0.000363196372 0.005667627  0.000000000            0 0.0076
## [585,] -0.000624412262 0.009777438  0.000000000            0 0.0088
## [586,] -0.001666836080 0.018446021  0.000000000            0 0.0124
## [587,] -0.000299805067 0.007437948  0.000000000            0 0.0076
## [588,] -0.001216731885 0.014719263  0.000000000            0 0.0120
## [589,] -0.003197021653 0.024525555  0.000000000            0 0.0232
## [590,] -0.002652591484 0.030648401  0.000000000            0 0.0148
## [591,] -0.000802817842 0.014476080  0.000000000            0 0.0080
## [592,] -0.003029664869 0.025862735  0.000000000            0 0.0200
## [593,] -0.001571477204 0.017614322  0.000000000            0 0.0116
## [594,] -0.001652086596 0.017048708  0.000000000            0 0.0128
## [595,] -0.001223139356 0.016442859  0.000000000            0 0.0108
## [596,] -0.000071310682 0.011106020  0.000000000            0 0.0056
## [597,] -0.003634705152 0.028577698  0.000000000            0 0.0204
## [598,] -0.001931167703 0.023176346  0.000000000            0 0.0124
## [599,] -0.000622286277 0.009720029  0.000000000            0 0.0064
## [600,] -0.000528397160 0.011415584  0.000000000            0 0.0104
## [601,] -0.000641582869 0.018060502  0.000000000            0 0.0076
## [602,] -0.001184921064 0.014149482  0.000000000            0 0.0108
## [603,] -0.000604810485 0.010819294  0.000000000            0 0.0076
## [604,] -0.000916969133 0.012587370  0.000000000            0 0.0084
## [605,] -0.000609473194 0.010282582  0.000000000            0 0.0088
## [606,] -0.000847543965 0.012352572  0.000000000            0 0.0088
## [607,]  0.000121560413 0.023920757  0.000000000            0 0.0072
## [608,] -0.000534069664 0.008191231  0.000000000            0 0.0072
## [609,] -0.001457899024 0.016173730  0.000000000            0 0.0108
## [610,] -0.000471093592 0.008582641  0.000000000            0 0.0072
## [611,] -0.001383984573 0.016520474  0.000000000            0 0.0124
## [612,] -0.000591767551 0.010125841  0.000000000            0 0.0072
## [613,] -0.000903789617 0.012752092  0.000000000            0 0.0108
## [614,] -0.001064492512 0.013334605  0.000000000            0 0.0100
## [615,] -0.000999262677 0.012416450  0.000000000            0 0.0108
## [616,] -0.000691417990 0.009556190  0.000000000            0 0.0084
## [617,] -0.002069877062 0.029702952  0.000000000            0 0.0120
## [618,] -0.001096636074 0.014243536  0.000000000            0 0.0096
## [619,] -0.000400250085 0.007450736  0.000000000            0 0.0084
## [620,] -0.000568853046 0.008871790  0.000000000            0 0.0068
## [621,] -0.000956654133 0.011165978  0.000000000            0 0.0112
## [622,] -0.001324412450 0.014263584  0.000000000            0 0.0152
## [623,] -0.000560012642 0.010428809  0.000000000            0 0.0084
## [624,] -0.001017123517 0.012908475  0.000000000            0 0.0096
## [625,] -0.000903764096 0.012843809  0.000000000            0 0.0100
## [626,] -0.000909749277 0.012686389  0.000000000            0 0.0112
## [627,] -0.000132577527 0.006061551  0.000000000            0 0.0060
## [628,] -0.003355496395 0.049421198  0.000000000            0 0.0164
## [629,] -0.000926762669 0.013299958  0.000000000            0 0.0116
## [630,] -0.000914038090 0.013886648  0.000000000            0 0.0096
## [631,] -0.000644291797 0.009580589  0.000000000            0 0.0076
## [632,] -0.002165540128 0.022071391  0.000000000            0 0.0156
## [633,] -0.001324075494 0.015517200  0.000000000            0 0.0140
## [634,]  0.000034985623 0.017421687  0.000000000            0 0.0068
## [635,] -0.000575394672 0.011133631  0.000000000            0 0.0072
## [636,] -0.002664580589 0.026807377  0.000000000            0 0.0152
## [637,] -0.000510186085 0.008031330  0.000000000            0 0.0096
## [638,] -0.000763531779 0.009113382  0.000000000            0 0.0092
## [639,] -0.000849372656 0.011834008  0.000000000            0 0.0092
## [640,] -0.001527857870 0.017832980  0.000000000            0 0.0124
## [641,] -0.000527503604 0.011180146  0.000000000            0 0.0080
## [642,] -0.000581529731 0.007163633  0.000000000            0 0.0096
## [643,] -0.000624440986 0.009563695  0.000000000            0 0.0080
## [644,] -0.001319846769 0.022909481  0.000000000            0 0.0112
## [645,] -0.001199608038 0.014915605  0.000000000            0 0.0100
## [646,] -0.000699012018 0.011857533  0.000000000            0 0.0056
## [647,] -0.000569431070 0.008176111  0.000000000            0 0.0080
## [648,] -0.001901123990 0.018309208  0.000000000            0 0.0148
## [649,] -0.001304170178 0.014229511  0.000000000            0 0.0148
## [650,] -0.000664581489 0.010923451  0.000000000            0 0.0072
## [651,] -0.003088401033 0.029030688  0.000000000            0 0.0176
## [652,] -0.001739302165 0.020101328  0.000000000            0 0.0124
## [653,] -0.000416112616 0.008469129  0.000000000            0 0.0068
## [654,] -0.000544329669 0.010832385  0.000000000            0 0.0068
## [655,] -0.000473985973 0.007364331  0.000000000            0 0.0060
## [656,] -0.000394011762 0.007090003  0.000000000            0 0.0064
## [657,] -0.000435116764 0.007934774  0.000000000            0 0.0056
## [658,] -0.001163813879 0.014134053  0.000000000            0 0.0128
## [659,] -0.000577922788 0.010281590  0.000000000            0 0.0092
## [660,] -0.001085381657 0.013179701  0.000000000            0 0.0100
## [661,]  0.000680647181 0.032562419  0.000000000            0 0.0092
## [662,] -0.000513777557 0.007786526  0.000000000            0 0.0076
## [663,] -0.001204616672 0.015391938  0.000000000            0 0.0100
## [664,] -0.000394294193 0.007145708  0.000000000            0 0.0072
## [665,] -0.000780183989 0.011746811  0.000000000            0 0.0068
## [666,] -0.000137846973 0.009613323  0.000000000            0 0.0068
## [667,] -0.000794393036 0.010563236  0.000000000            0 0.0092
## [668,] -0.000421507949 0.008700923  0.000000000            0 0.0076
## [669,] -0.000730749580 0.010924732  0.000000000            0 0.0068
## [670,] -0.000537917335 0.009223214  0.000000000            0 0.0072
## [671,] -0.001958481117 0.036191454  0.000000000            0 0.0116
## [672,] -0.000718161398 0.009996088  0.000000000            0 0.0088
## [673,] -0.000626035548 0.009919222  0.000000000            0 0.0100
## [674,] -0.000372587252 0.008695753  0.000000000            0 0.0056
## [675,] -0.000149203703 0.007183923  0.000000000            0 0.0064
## [676,] -0.000833097955 0.012832621  0.000000000            0 0.0096
## [677,] -0.000625209840 0.012795769  0.000000000            0 0.0080
## [678,] -0.001521342721 0.017961143  0.000000000            0 0.0112
## [679,] -0.001558532637 0.020233226  0.000000000            0 0.0140
## [680,] -0.000327036457 0.014040691  0.000000000            0 0.0064
## [681,] -0.000270399548 0.008051421  0.000000000            0 0.0060
## [682,] -0.001250793161 0.015916474  0.000000000            0 0.0104
## [683,] -0.001342914113 0.016352512  0.000000000            0 0.0108
## [684,] -0.000835891110 0.014226527  0.000000000            0 0.0068
## [685,] -0.001299778994 0.018951716  0.000000000            0 0.0088
## [686,] -0.000803979336 0.013422881  0.000000000            0 0.0080
## [687,] -0.000836207277 0.013457492  0.000000000            0 0.0076
## [688,] -0.000220066126 0.010041542  0.000000000            0 0.0056
## [689,] -0.000318971870 0.006644023  0.000000000            0 0.0060
## [690,] -0.001350612074 0.016579808  0.000000000            0 0.0112
## [691,] -0.000519060763 0.018652827  0.000000000            0 0.0084
## [692,] -0.001587947868 0.019732748  0.000000000            0 0.0116
## [693,] -0.000998190727 0.014113425  0.000000000            0 0.0128
## [694,] -0.001124465902 0.014207001  0.000000000            0 0.0096
## [695,] -0.000387307293 0.006318189  0.000000000            0 0.0044
## [696,] -0.001323131529 0.014070725  0.000000000            0 0.0132
## [697,] -0.000408633146 0.007062669  0.000000000            0 0.0076
## [698,] -0.000974316003 0.016531763  0.000000000            0 0.0068
## [699,] -0.000774622017 0.011352796  0.000000000            0 0.0096
## [700,] -0.002212975406 0.021648956  0.000000000            0 0.0164
## [701,] -0.000982937410 0.012643314  0.000000000            0 0.0092
## [702,] -0.002277843006 0.025129725  0.000000000            0 0.0152
## [703,] -0.003322910152 0.029006182  0.000000000            0 0.0192
## [704,] -0.000569439372 0.010626810  0.000000000            0 0.0088
## [705,] -0.001387367401 0.015078211  0.000000000            0 0.0136
## [706,] -0.001231921863 0.016324356  0.000000000            0 0.0108
## [707,] -0.000611374148 0.008170735  0.000000000            0 0.0076
## [708,] -0.000759857913 0.010703034  0.000000000            0 0.0076
## [709,] -0.000900980439 0.012654887  0.000000000            0 0.0088
## [710,] -0.001757922248 0.019235227  0.000000000            0 0.0128
## [711,] -0.000588101871 0.010188308  0.000000000            0 0.0068
## [712,] -0.000290507757 0.006254415  0.000000000            0 0.0068
## [713,] -0.001063737568 0.016027229  0.000000000            0 0.0088
## [714,] -0.000935887484 0.012249577  0.000000000            0 0.0088
## [715,] -0.000394520996 0.008274681  0.000000000            0 0.0056
## [716,] -0.000151695400 0.015859241  0.000000000            0 0.0076
## [717,] -0.002763723722 0.028074895  0.000000000            0 0.0164
## [718,]  0.000401801112 0.023167887  0.000000000            0 0.0056
## [719,] -0.001129521719 0.013565268  0.000000000            0 0.0128
## [720,] -0.000546422994 0.009201072  0.000000000            0 0.0076
## [721,] -0.000980097985 0.013118434  0.000000000            0 0.0092
## [722,] -0.000551255727 0.009679981  0.000000000            0 0.0056
## [723,] -0.001456317038 0.016586021  0.000000000            0 0.0116
## [724,] -0.000521684937 0.008555513  0.000000000            0 0.0076
## [725,] -0.002050698774 0.028057492  0.000000000            0 0.0112
## [726,] -0.001322914727 0.016443188  0.000000000            0 0.0108
## [727,] -0.000235417818 0.005926543  0.000000000            0 0.0060
## [728,] -0.001057126308 0.015723877  0.000000000            0 0.0084
## [729,] -0.001254607816 0.015663196  0.000000000            0 0.0132
## [730,] -0.001377979462 0.015254448  0.000000000            0 0.0144

5 Linear models for each predictor

5.1 Screening the exposures

None of the exposures had a PIP > 0.5. Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(adiposity ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Adiposity.csv"))

5.2 Linear model for distance to waste sites

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_waste_lm <- lm(adiposity ~ dist_m_waste_site + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_waste_lm)
## 
## Call:
## lm(formula = adiposity ~ dist_m_waste_site + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.1152 -2.6385 -0.1678  2.7592 15.5462 
## 
## Coefficients:
##                    Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)        10.02150    3.90254   2.568        0.0104 *  
## dist_m_waste_site   0.36281    0.15149   2.395        0.0169 *  
## lat                12.72052  148.21325   0.086        0.9316    
## lon                -5.73270   70.63195  -0.081        0.9353    
## lat_lon_int        15.09494  178.21522   0.085        0.9325    
## latina_re          -0.48057    0.40192  -1.196        0.2322    
## black_re           -0.27689    0.43874  -0.631        0.5282    
## other_re           -0.87609    0.57642  -1.520        0.1290    
## ed_no_hs            1.23866    0.65067   1.904        0.0573 .  
## ed_hs               1.07560    0.58154   1.850        0.0648 .  
## ed_aa               0.81041    0.51063   1.587        0.1129    
## ed_4yr              0.07400    0.42583   0.174        0.8621    
## low_bmi            -0.42315    0.80718  -0.524        0.6003    
## ovwt_bmi            0.52044    0.34122   1.525        0.1276    
## obese_bmi           1.24425    0.38806   3.206        0.0014 ** 
## concep_spring       0.29517    0.39971   0.738        0.4605    
## concep_summer       0.13378    0.39414   0.339        0.7344    
## concep_fall         0.03868    0.39069   0.099        0.9212    
## concep_2010        -0.55100    3.90233  -0.141        0.8878    
## concep_2011        -1.11020    3.90475  -0.284        0.7762    
## concep_2012        -1.36997    3.89964  -0.351        0.7255    
## concep_2013        -1.04232    3.90481  -0.267        0.7896    
## maternal_age        0.79576    0.18829   4.226 0.00002669215 ***
## any_smoker         -0.88965    0.53394  -1.666        0.0961 .  
## smokeSH            -0.09976    0.37929  -0.263        0.7926    
## mean_cpss          -0.06078    0.16639  -0.365        0.7150    
## mean_epsd          -0.19513    0.16928  -1.153        0.2494    
## male               -1.37099    0.27394  -5.005 0.00000069768 ***
## days_to_peapod      0.82688    0.13914   5.943 0.00000000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.773 on 751 degrees of freedom
## Multiple R-squared:  0.1402, Adjusted R-squared:  0.1082 
## F-statistic: 4.375 on 28 and 751 DF,  p-value: 0.000000000001403
plot(ad_waste_lm)

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

5.3 Linear model for respiratory hospitalization rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_res_lm <- lm(adiposity ~ res_rate_adj + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_res_lm)
## 
## Call:
## lm(formula = adiposity ~ res_rate_adj + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.7234 -2.5753 -0.2042  2.7269 16.1631 
## 
## Coefficients:
##                 Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)      9.67278    3.90877   2.475       0.01356 *  
## res_rate_adj    -0.24964    0.15140  -1.649       0.09960 .  
## lat             36.76972  148.72945   0.247       0.80480    
## lon            -17.28087   70.88017  -0.244       0.80745    
## lat_lon_int     44.14802  178.83348   0.247       0.80508    
## latina_re       -0.38383    0.40356  -0.951       0.34185    
## black_re        -0.19174    0.43981  -0.436       0.66298    
## other_re        -0.81865    0.57851  -1.415       0.15746    
## ed_no_hs         1.31937    0.65663   2.009       0.04486 *  
## ed_hs            1.15845    0.58646   1.975       0.04860 *  
## ed_aa            0.94161    0.51282   1.836       0.06673 .  
## ed_4yr           0.13362    0.42564   0.314       0.75367    
## low_bmi         -0.50970    0.80895  -0.630       0.52884    
## ovwt_bmi         0.47288    0.34205   1.382       0.16723    
## obese_bmi        1.26674    0.38909   3.256       0.00118 ** 
## concep_spring    0.31816    0.40032   0.795       0.42700    
## concep_summer    0.11014    0.39513   0.279       0.78053    
## concep_fall      0.04729    0.39147   0.121       0.90387    
## concep_2010     -0.33604    3.90881  -0.086       0.93151    
## concep_2011     -0.86851    3.91105  -0.222       0.82432    
## concep_2012     -1.16914    3.90637  -0.299       0.76480    
## concep_2013     -0.83812    3.91148  -0.214       0.83039    
## maternal_age     0.76831    0.18806   4.086 0.00004870493 ***
## any_smoker      -0.86685    0.53535  -1.619       0.10582    
## smokeSH         -0.09518    0.38007  -0.250       0.80233    
## mean_cpss       -0.04247    0.16639  -0.255       0.79861    
## mean_epsd       -0.19821    0.16980  -1.167       0.24346    
## male            -1.32203    0.27511  -4.805 0.00000186532 ***
## days_to_peapod   0.82938    0.13942   5.949 0.00000000414 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.781 on 751 degrees of freedom
## Multiple R-squared:  0.1368, Adjusted R-squared:  0.1046 
## F-statistic: 4.251 on 28 and 751 DF,  p-value: 0.000000000004589
plot(ad_res_lm)

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

5.4 Linear model for property crime rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_pcrime_lm <- lm(adiposity ~ property_crime_rate + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_pcrime_lm)
## 
## Call:
## lm(formula = adiposity ~ property_crime_rate + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6783 -2.6161 -0.1684  2.7626 15.8124 
## 
## Coefficients:
##                      Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)           9.65291    3.90266   2.473       0.01360 *  
## property_crime_rate  -0.31479    0.13972  -2.253       0.02455 *  
## lat                  31.91270  148.29287   0.215       0.82967    
## lon                 -14.93929   70.67019  -0.211       0.83264    
## lat_lon_int          38.29701  178.30884   0.215       0.83000    
## latina_re            -0.46827    0.40192  -1.165       0.24435    
## black_re             -0.29343    0.43940  -0.668       0.50446    
## other_re             -0.93457    0.57731  -1.619       0.10590    
## ed_no_hs              1.19286    0.65058   1.834       0.06712 .  
## ed_hs                 1.07542    0.58181   1.848       0.06494 .  
## ed_aa                 0.91635    0.51063   1.795       0.07313 .  
## ed_4yr                0.18710    0.42523   0.440       0.66007    
## low_bmi              -0.46686    0.80730  -0.578       0.56324    
## ovwt_bmi              0.46817    0.34145   1.371       0.17074    
## obese_bmi             1.25965    0.38829   3.244       0.00123 ** 
## concep_spring         0.32470    0.39966   0.812       0.41680    
## concep_summer         0.14151    0.39434   0.359       0.71980    
## concep_fall           0.02365    0.39096   0.060       0.95179    
## concep_2010          -0.18066    3.90305  -0.046       0.96309    
## concep_2011          -0.71684    3.90537  -0.184       0.85441    
## concep_2012          -1.03992    3.90058  -0.267       0.78984    
## concep_2013          -0.72418    3.90556  -0.185       0.85295    
## maternal_age          0.77043    0.18770   4.104 0.00004496165 ***
## any_smoker           -0.86307    0.53440  -1.615       0.10672    
## smokeSH              -0.10116    0.37946  -0.267       0.78985    
## mean_cpss            -0.03802    0.16586  -0.229       0.81874    
## mean_epsd            -0.20551    0.16917  -1.215       0.22481    
## male                 -1.40426    0.27486  -5.109 0.00000041128 ***
## days_to_peapod        0.82385    0.13921   5.918 0.00000000495 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.775 on 751 degrees of freedom
## Multiple R-squared:  0.1395, Adjusted R-squared:  0.1074 
## F-statistic: 4.348 on 28 and 751 DF,  p-value: 0.000000000001819
plot(ad_pcrime_lm)
## Warning: not plotting observations with leverage one:
##   1

5.5 Linear model for %unemployed rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_unemp_lm <- lm(adiposity ~ pct_unemp + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_unemp_lm)
## 
## Call:
## lm(formula = adiposity ~ pct_unemp + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6136 -2.5739 -0.1227  2.6643 15.9796 
## 
## Coefficients:
##                 Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)      9.66018    3.90718   2.472      0.013641 *  
## pct_unemp       -0.27813    0.15209  -1.829      0.067843 .  
## lat             18.84591  148.40739   0.127      0.898984    
## lon             -8.68304   70.72418  -0.123      0.902319    
## lat_lon_int     22.61179  178.44698   0.127      0.899200    
## latina_re       -0.29709    0.40929  -0.726      0.468151    
## black_re        -0.09939    0.44480  -0.223      0.823243    
## other_re        -0.80122    0.57866  -1.385      0.166583    
## ed_no_hs         1.32492    0.65577   2.020      0.043695 *  
## ed_hs            1.19286    0.58775   2.030      0.042755 *  
## ed_aa            0.97771    0.51414   1.902      0.057602 .  
## ed_4yr           0.19854    0.42625   0.466      0.641502    
## low_bmi         -0.41917    0.80868  -0.518      0.604377    
## ovwt_bmi         0.48223    0.34170   1.411      0.158581    
## obese_bmi        1.29104    0.38955   3.314      0.000963 ***
## concep_spring    0.29460    0.40051   0.736      0.462232    
## concep_summer    0.11011    0.39493   0.279      0.780471    
## concep_fall      0.04963    0.39131   0.127      0.899106    
## concep_2010     -0.39542    3.90747  -0.101      0.919421    
## concep_2011     -0.91640    3.90959  -0.234      0.814740    
## concep_2012     -1.21936    3.90492  -0.312      0.754928    
## concep_2013     -0.85571    3.90990  -0.219      0.826821    
## maternal_age     0.74830    0.18780   3.985 0.00007418007 ***
## any_smoker      -0.93043    0.53505  -1.739      0.082455 .  
## smokeSH         -0.08158    0.38005  -0.215      0.830094    
## mean_cpss       -0.03983    0.16616  -0.240      0.810619    
## mean_epsd       -0.19942    0.16960  -1.176      0.240031    
## male            -1.35414    0.27429  -4.937 0.00000097868 ***
## days_to_peapod   0.83228    0.13939   5.971 0.00000000364 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.779 on 751 degrees of freedom
## Multiple R-squared:  0.1375, Adjusted R-squared:  0.1054 
## F-statistic: 4.277 on 28 and 751 DF,  p-value: 0.000000000003591
plot(ad_unemp_lm)
## Warning: not plotting observations with leverage one:
##   1